perm filename M[AM,DBL] blob
sn#196172 filedate 1976-01-15 generic text, type T, neo UTF8
(FILECREATED "31-DEC-75 18:01:08" <LENAT>M.;5 109650
changes to: MCOMS EXPLAIN IDEAL LOGQUO TABLE CUT UNFAC ROUND TAU1
QTABLE FIXEDNS
previous date: "31-DEC-75 15:29:57" <LENAT>M.;4)
(LISPXPRINT (QUOTE MCOMS)
T T)
(RPAQQ MCOMS
((FNS ISPRIME LOGN N MIN NOFT AM1 TABLE AKM1 CUT GETMINN TAU
FAC1 FACS UNFAC ROUND TAU1 QTABLE)
PRIMES LOGS PRODLOGS LOGCKS LOGLOGS SUMLOGLOGS CKS KCKS EKCKS
PPRODS EXPLAIN SUMLOGS CUT GLOBALVARS LOGQUO MINN IDEAL
IDEAL2 FIXEDNS))
(DEFINEQ
(ISPRIME
[LAMBDA (N)
(FOR J FROM 2 TO (FIX (SQRT N))
ALWAYS (NOT (ZEROP (REMAINDER N J])
(LOGN
[LAMBDA (K TT)
(DIFFERENCE (FTIMES (CAR (FNTH KCKS K))
(EXPT TT (FQUOTIENT 1.0 K)))
(CAR (FNTH SUMLOGS K])
(N
[LAMBDA (K TT L)
(ANTILOG (COND
((ILESSP (SETQ L (LOGN K TT))
88)
L)
(T 88])
(MIN
[LAMBDA (L I V MI)
(SETQ I 1)
(SETQ MI 1)
(SETQ V (CAR L))
[MAPC (CDR L)
(FUNCTION (LAMBDA (X)
(SETQ I (ADD1 I))
(COND
((ILESSP X V)
(SETQ V X)
(SETQ MI I]
(LIST MI V])
(NOFT
[LAMBDA (TT N K)
(SETQ K 1)
(SETQ N (N K TT))
[PROG NIL
L1 (SETQ K (ADD1 K))
(* COND ((NOT (FGTP (SETQ N1
(N K TT)) N)) (SETQ N N1) (GO L1)))
(COND
((FGTP (AKM1 K TT)
(CUT K))
(SETQ N (N K TT))
(GO L1]
(SETQ K (SUB1 K))
(LIST N K])
(AM1
[LAMBDA (K TT NUME)
[SETQ NUME (FTIMES (CAR (FNTH CKS K))
(EXPT TT (FQUOTIENT 1.0 K]
(FOR I FROM 1 TO K COLLECT (DIFFERENCE (FQUOTIENT
NUME
(CAR (FNTH LOGS I)))
1])
(TABLE
[LAMBDA (T1 T2 C A1 A2 N2)
(COND
(C (SETQ CUT C)))
(FOR TT FROM T1 TO T2
DO (PROGN (SETQ NK (NOFT TT))
(PRIN1 (QUOTE T=))
(PRIN1 TT)
(SPACES 2)
(PRIN1 (QUOTE K=))
(PRIN1 (CADR NK))
(SPACES 2)
(PRIN1 (QUOTE N=))
(PRIN1 (CAR NK))
(SPACES 2)
(PRIN1 (QUOTE AM1S=))
(PRIN1 (SETQ A1 (AM1 (CADR NK)
TT)))
(SPACES 2)
(PRIN1 (QUOTE FIXED-TO:))
[PRIN1 (SETQ A2 (MAPCAR A1 (QUOTE ROUND]
(SPACES 2)
(PRIN1 (QUOTE FIXED-N=))
(PRIN1 (SETQ N2 (UNFAC A2)))
(TERPRI)
(COND
((SASSOC N2 FIXEDNS))
(T (NCONC1 FIXEDNS (LIST N2 A2])
(AKM1
[LAMBDA (K TT NUME)
[SETQ NUME (FTIMES (CAR (FNTH CKS K))
(EXPT TT (FQUOTIENT 1.0 K]
(DIFFERENCE (FQUOTIENT NUME (CAR (FNTH LOGS K)))
1])
(CUT
[LAMBDA (K) (* CAR (FNTH LOGQUO K))
CUT])
(GETMINN
[LAMBDA (N1 N2)
(FOR JJ FROM N1 TO N2 DO (SETQ T3 (TAU JJ))
(COND
((ZEROP (CAR (FNTH MINN T3)))
(RPLACA (FNTH MINN T3)
JJ])
(TAU
[LAMBDA (N)
(APPLY (QUOTE ITIMES)
(MAPCAR (FACS N)
(QUOTE ADD1])
(FAC1
[LAMBDA (N I J)
(SETQ J (CAR (FNTH PRIMES I)))
(COND
((ZEROP (REMAINDER N J))
(SETQ N (IQUOTIENT N J))
[RPLACA (FNTH FS I)
(ADD1 (CAR (FNTH FS I]
(FAC1 N I))
((ILESSP J N)
(FAC1 N (ADD1 I])
(FACS
[LAMBDA (N)
(SETQ FS (FOR J FROM 1 TO N COLLECT 0))
(FAC1 N 1)
FS])
(UNFAC
[LAMBDA (L V)
(SETQ V 1)
[MAP2C L PRIMES (FUNCTION (LAMBDA (ALPH P)
(SETQ V (ITIMES V (EXPT P ALPH]
V])
(ROUND
[LAMBDA (X)
(FIX (FPLUS X .5])
(TAU1
[LAMBDA (L V)
(SETQ V 1)
[MAPC L (FUNCTION (LAMBDA (X)
(SETQ V (ITIMES V (ADD1 X]
V])
(QTABLE
[LAMBDA (T1 T2 B C A1 A2 N2 T3)
(COND
(C (SETQ CUT C)))
(OR B (SETQ B 1))
(FOR TT FROM T1 TO T2 BY B
DO (PROGN (SETQ NK (NOFT TT))
(PRIN1 (QUOTE T=))
(PRIN1 TT)
(SPACES 2)
(PRIN1 (QUOTE K=))
(PRIN1 (CADR NK))
(SPACES 2)
(PRIN1 (QUOTE N=))
(PRIN1 (CAR NK))
(SPACES 2)
(SETQ A1 (AM1 (CADR NK)
TT))
(SETQ A2 (MAPCAR A1 (QUOTE ROUND)))
(SETQ N2 (UNFAC A2))
[COND
((SASSOC N2 FIXEDNS))
(T (PRIN1 (QUOTE NEW-FIXED-AM1S=))
(PRIN1 A2)
(SPACES 2)
(PRIN1 (QUOTE GIVE-N=))
(PRIN1 N2)
(PRIN1 (QUOTE ,T=))
(PRIN1 (SETQ T3 (TAU1 A2)))
(NCONC1 FIXEDNS (LIST N2 A2 T3]
(TERPRI])
)
(RPAQQ PRIMES
(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79
83 89 97 101 103 107 109 113 127 131 137 139 149 151 157
163 167 173 179 181 191 193 197 199 211 223 227 229 233 239
241 251 257 263 269 271 277 281 283 293 307 311 313 317 331
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431 433 439 443 449 457 461 463 467 479 487 491 499 503 509
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617 619 631 641 643 647 653 659 661 673 677 683 691 701 709
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1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093
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1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999
2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087
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2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281
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2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671
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2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833
2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927
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3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163
3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253
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3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019
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4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441
4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523
4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643
4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733
4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861
4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957
4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039
5051 5059))
(RPAQQ LOGS
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2.944439 3.135494 3.367296 3.433987 3.610918
3.713572 3.7612 3.850148 3.970292 4.077537 4.110874
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5.855072 5.866468 5.883322 5.905362 5.921578
5.937536 5.948035 5.963579 5.983936 5.993961
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(RPAQQ PRODLOGS
(.6931472 .7615 1.225587 2.384882 5.718697 14.66817 41.55805
122.3651 383.6752 1291.948 4436.533 16019.95
59491.26 223758.5 861503.3 3.42042E6 1.394689E7
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5.366284E24 2.824109E25 1.492034E26 7.897792E26
4.226786E27 2.285496E28 1.23987E29 6.737109E29
3.672424E30 2.01119E31 1.103097E32 6.095109E32
3.382222E33 1.884626E34 1.054394E35 5.90684E35
3.322017E36 1.873071E37 1.057432E38))
(RPAQQ LOGCKS
(-.3665129 -.1362325 .06780663 .2172874 .3487482 .4476133
.5324416 .6008762 .6610885 .7163906 .7634207
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1.974216 1.974466 1.974716 1.974965 1.975214
1.975463 1.975711))
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1.994945 1.995641 1.995988 1.996678 1.997021
1.998215 1.998555 1.999061 1.99923 1.999566
2.000069 2.000236 2.000736 2.001564 2.003203
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2.006574 2.007363 2.008303 2.008459 2.009235
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2.013042 2.013341 2.01349 2.014383 2.015121
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2.019456 2.019598 2.019881 2.020023 2.020726
2.021565 2.021983 2.022399 2.023637 2.023774
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2.02938 2.03003 2.030159 2.030805 2.031702 2.032339
2.032719 2.033477 2.033602 2.033853 2.033979
2.034603 2.035348 2.035472 2.036457 2.036579
2.036946 2.03719 2.037312 2.037918 2.038402
2.039481 2.040905 2.041141 2.041494 2.041962
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2.048768 2.049097 2.049317 2.049645 2.050407
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2.062641 2.063031 2.063225 2.063805 2.064478
2.064956 2.065052 2.065242 2.065623 2.065907
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2.067318 2.067505 2.067598 2.067877 2.068341
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243.7842 245.6935 247.6036 249.514 251.4251
253.3385 255.2527 257.1671 259.0823 261.0007
262.9197 264.8401 266.762 268.6852 270.609 272.5337
274.4594 276.3871 278.3155 280.2448 282.1749
284.1063 286.0385 287.9724 289.9069 291.8423
293.7779 295.715 297.6523 299.5905 301.53 303.4698
305.411 307.3525 309.2947 311.2394 313.1845 315.13
317.0759 319.0227 320.9702 322.9187 324.868
326.8181 328.7709 330.7239 332.6782 334.6334
336.5898 338.547 340.5049 342.4637 344.4239
346.3846 348.3459 350.308 352.2703 354.2333
356.1976 358.163 360.1304 362.0981 364.0662
366.0349 368.0039 369.9735 371.9435 373.9137
375.8844 377.8563 379.8285 381.8013 383.7776
385.7545 387.732 389.7103 391.6904 393.6715
395.6539 397.6368 399.6198 401.6032 403.5872
405.572 407.5571 409.5424 411.5283 413.5153
415.5032 417.4914 419.4799 421.4685 423.4576
425.4472 427.4378 429.4296 431.4221 433.4156
435.4097 437.4041 439.399 441.3947 443.3907
445.3873 447.3844 449.3826 451.3811 453.3802
455.3794 457.379 459.3791 461.3793 463.38 465.3816
467.3848 469.3885 471.3925 473.3967 475.4028
477.4092 479.4157 481.4231 483.4314 485.4399
487.4491 489.4589 491.4693 493.48 495.4912 497.5038
499.5169 501.5302 503.5437 505.5581 507.5732
509.5892 511.6058 513.6235 515.6423 517.6614
519.6809 521.7005 523.7203 525.7404 527.7611
529.7826 531.8046 533.827 535.8507 537.8744
539.8993 541.9243 543.9508 545.9776 548.005
550.0328 552.0609 554.0891 556.1176 558.1465
560.1759 562.2059 564.2361 566.2669 568.2986
570.3309 572.3636 574.3971 576.4307 578.4646
580.4985 582.5331 584.5685 586.604 588.6404 590.677
592.7139 594.7511 596.7884 598.8263 600.8647
602.9042 604.9451 606.9863 609.0277 611.0697
613.1126 615.1556 617.1988 619.2425 621.2872
623.3319 625.3768 627.4223 629.468 631.5141
633.5604 635.6074 637.6545 639.7028 641.7515
643.8002 645.8493 647.8987 649.9483 651.9987
654.0494 656.1004 658.1514 660.2028 662.2544
664.3063 666.3589 668.4117 670.4649 672.5189
674.573 676.6275 678.6825 680.738 682.7938 684.8499
686.9072 688.9655 691.0242 693.0834 695.1428
697.2025 699.2622 701.3223 703.3835 705.4452
707.5071 709.5697 711.6328 713.696 715.7598
717.8243 719.8892 721.9543 724.0195 726.0851
728.151 730.2172 732.2836 734.3501 736.4167
738.4837 740.551 742.6185 744.6861 746.7539
748.8223 750.8907 752.9596 755.0288 757.0983
759.1684 761.2389 763.31 765.3812 767.4526 769.5242
771.596 773.6684 775.7414 777.8147 779.8882 781.962
784.0361 786.1104 788.1855 790.2609 792.3368
794.4129 796.4893 798.566 800.6432 802.7208
804.7991 806.8775 808.9562 811.0351 813.1141
815.1943 817.2746 819.3553 821.4363 823.5175
825.5993 827.6812 829.7635 831.8462 833.9292
836.0126 838.0963 840.1802 842.2648 844.3499
846.4351 848.5209 850.6077 852.6947 854.7817
856.8692 858.957 861.0449 863.1333 865.2219
867.3108 869.3999 871.4893 873.5795 875.6698
877.7602 879.8508 881.9417 884.0338 886.1259
888.2182 890.3108 892.4035 894.4965 896.5896
898.6828 900.7765 902.8703 904.9646 907.0589
909.1536 911.2483 913.3437 915.4391 917.5351
919.6313 921.7282 923.8258 925.9235 928.0215
930.1195 932.2176 934.3158 936.4148 938.5141
940.6138 942.7137 944.8139 946.9142 949.0147
951.1153 953.2161 955.317 957.4183 959.5196
961.6214 963.7235 965.8257 967.9282 970.0312
972.1344 974.2377 976.3412 978.445 980.549 982.6532
984.7579 986.8631 988.9683 991.0736 993.1794
995.2854 997.3915 999.4979 1001.605 1003.712
1005.819 1007.926 1010.034 1012.142 1014.251
1016.359 1018.469 1020.578 1022.687 1024.797
1026.907 1029.018 1031.129 1033.239 1035.35
1037.462 1039.574 1041.685 1043.798 1045.91
1048.023 1050.136 1052.249 1054.362 1056.476
1058.589 1060.703 1062.817 1064.931 1067.047
1069.162 1071.278 1073.393 1075.509 1077.626
1079.742 1081.858 1083.975 1086.092 1088.209
1090.327 1092.445 1094.563 1096.681 1098.8 1100.919
1103.038 1105.157 1107.277 1109.396 1111.517
1113.637 1115.757 1117.878 1119.999 1122.121
1124.243 1126.365 1128.487 1130.609 1132.732
1134.854 1136.977 1139.1 1141.223 1143.347 1145.47
1147.594 1149.718 1151.842 1153.967 1156.092
1158.217 1160.343 1162.469 1164.595 1166.721
1168.848 1170.975 1173.102 1175.229 1177.357
1179.485 1181.613 1183.741 1185.87 1187.999
1190.128 1192.257 1194.386 1196.516 1198.646
1200.776 1202.906 1205.037 1207.167 1209.298
1211.43 1213.561 1215.693 1217.825 1219.957
1222.089 1224.222 1226.355 1228.489 1230.622
1232.755 1234.889 1237.023 1239.156 1241.291
1243.425 1245.559 1247.694 1249.83 1251.965 1254.1
1256.236 1258.372 1260.508 1262.645 1264.782
1266.919 1269.056 1271.194 1273.331 1275.468
1277.606 1279.744 1281.883 1284.022 1286.161
1288.301 1290.44 1292.58 1294.72 1296.861 1299.001
1301.142 1303.283 1305.424 1307.565 1309.706
1311.847 1313.989 1316.13 1318.272 1320.414
1322.557 1324.699 1326.841 1328.984 1331.126
1333.269 1335.413 1337.556))
(RPAQQ CKS
(.6931472 .8726397 1.070158 1.242701 1.417292 1.564574
1.703085 1.823716 1.936899 2.047031 2.145603
2.240724 2.329516 2.410611 2.487046 2.560825
2.631863 2.697881 2.76163 2.822223 2.879081 2.934195
2.986897 3.038022 3.088174 3.136264 3.181958
3.225928 3.267857 3.308326 3.349274 3.388798
3.427301 3.464239 3.500828 3.536001 3.570345
3.603889 3.636447 3.66828 3.699413 3.7295 3.759314
3.788167 3.816273 3.843513 3.870681 3.897732 3.92412
3.949748 3.974777 3.99935 4.023255 4.046963 4.070256
4.093149 4.115651 4.13759 4.15917 4.180316 4.200958
4.221448 4.241934 4.262024 4.281661 4.300933
4.320195 4.33917 4.357992 4.376415 4.394514 4.412358
4.430009 4.447416 4.464585 4.48147 4.49813 4.514619
4.530846 4.54691 4.562857 4.578514 4.59406 4.609329
4.62441 4.639269 4.65395 4.668496 4.682833 4.696932
4.710834 4.724685 4.738414 4.751957 4.765382
4.778629 4.791732 4.804786 4.81764 4.830531 4.843284
4.855956 4.868495 4.880902 4.893129 4.905232
4.917262 4.92917 4.940959 4.952585 4.964097 4.975498
4.986767 4.997886 5.008965 5.019982 5.030856
5.041609 5.052264 5.062823 5.073249 5.08364 5.09392
5.104111 5.114232 5.1243 5.1343 5.144248 5.154127
5.163923 5.173636 5.183252 5.192804 5.202277
5.211658 5.220977 5.230207 5.239421 5.24859 5.257727
5.266764 5.275757 5.284653 5.293467 5.302186
5.310865 5.319528 5.328114 5.33661 5.34503 5.353436
5.361768 5.370016 5.378192 5.386389 5.394516
5.402595 5.410638 5.418634 5.426564 5.434437
5.442255 5.450059 5.4578 5.465486 5.47312 5.480712
5.488252 5.49577 5.503228 5.510636 5.517976 5.525287
5.532531 5.539729 5.546897 5.554003 5.561079
5.568094 5.575065 5.582041 5.588965 5.59583 5.602645
5.609417 5.616149 5.622846 5.629504 5.636121
5.642758 5.64934 5.655897 5.662423 5.668923 5.675385
5.681809 5.688203 5.694579 5.700911 5.707207
5.713466 5.719677 5.725852 5.732012 5.738149
5.744288 5.750381 5.756434 5.762453 5.768426
5.774367 5.78027 5.786129 5.791951 5.797758 5.803524
5.809258 5.815039 5.82079 5.82651 5.832204 5.8379
5.843576 5.849243 5.854874 5.860467 5.866025
5.871554 5.87706 5.882532 5.887968 5.893375 5.89877
5.904146 5.909487 5.914796 5.92007 5.925313 5.93053
5.935736 5.940929 5.946102 5.951262 5.956398
5.961504 5.966586 5.971648 5.976682 5.981696
5.986683 5.991662 5.996614 6.001543 6.006441
6.011312 6.016162 6.020981 6.025778 6.030561 6.03535
6.040116 6.044858 6.049571 6.054295 6.058995
6.063667 6.068326 6.072974 6.077595 6.082203
6.086794 6.091365 6.095917 6.100448 6.10498 6.109493
6.113983 6.118447 6.122902 6.127344 6.131778
6.136195 6.14061 6.145018 6.149408 6.153777 6.158121
6.162444 6.166743 6.17103 6.175309 6.17957 6.183814
6.188058 6.192279 6.196496 6.200692 6.204892
6.209076 6.213246 6.217399 6.221532 6.225644
6.229736 6.233816 6.237879 6.241932 6.245963
6.249984 6.254 6.258005 6.261995 6.265977 6.269939
6.273883 6.277807 6.281721 6.285627 6.289514
6.293399 6.297264 6.301114 6.304948 6.308763
6.312568 6.316362 6.320155 6.323955 6.327739
6.331509 6.335267 6.339023 6.342761 6.346482
6.350193 6.353901 6.357591 6.361266 6.364929 6.36858
6.372217 6.37584 6.379456 6.383055 6.386658 6.390248
6.393821 6.397382 6.400929 6.404463 6.407993
6.411511 6.415015 6.418503 6.421978 6.42544 6.428891
6.432335 6.435768 6.439189 6.442606 6.44601 6.449402
6.452789 6.456166 6.459532 6.462885 6.466246
6.469605 6.472957 6.4763 6.47963 6.482949 6.486254
6.489548 6.492845 6.496136 6.499413 6.502688
6.505954 6.509208 6.512456 6.515701 6.518938
6.522162 6.525373 6.528577 6.531769 6.534952
6.538124 6.541282 6.544428 6.547565 6.550694
6.553811 6.556916 6.560011 6.5631 6.566175 6.569245
6.572307 6.575358 6.578406 6.581448 6.584484
6.587509 6.590524 6.59353 6.596523 6.599514 6.602503
6.60548 6.60845 6.611411 6.614364 6.617307 6.62025
6.623185 6.626114 6.629035 6.631948 6.634853
6.637752 6.640647 6.643539 6.646422 6.649296
6.652162 6.655017 6.657878 6.660728 6.663573 6.66641
6.669239 6.672065 6.674881 6.67769 6.680496 6.683293
6.686087 6.688871 6.691647 6.694424 6.697196
6.699958 6.702718 6.705482 6.708238 6.710983
6.713724 6.716458 6.719183 6.721904 6.724618
6.727325 6.730024 6.732717 6.735411 6.738096
6.740772 6.743439 6.746102 6.748769 6.751428
6.754079 6.756724 6.759361 6.76199 6.764612 6.767225
6.769834 6.772436 6.775033 6.777622 6.780206
6.782781 6.785355 6.78792 6.790483 6.79304 6.795597
6.798153 6.800703 6.803245 6.805779 6.808305
6.810823 6.813342 6.815856 6.818366 6.82087 6.82337
6.825861 6.828345 6.830823 6.833292 6.835755
6.838215 6.840666 6.843113 6.845557 6.847992
6.850424 6.852853 6.855276 6.857692 6.860102
6.862507 6.864906 6.8673 6.869692 6.872081 6.874462
6.876837 6.879209 6.881576 6.883936 6.886291
6.888642 6.890989 6.89333 6.895665 6.898002 6.900333
6.902656 6.904976 6.907294 6.909605 6.911911
6.914217 6.916515 6.91881 6.921102 6.923389 6.925668
6.927944 6.930217 6.932484 6.934747 6.93701 6.939266
6.941517 6.943762 6.946 6.948234 6.95046 6.952684
6.954902 6.957121 6.95934 6.961557 6.963767 6.965971
6.968171 6.970365 6.972553 6.974736 6.97692 6.979098
6.98127 6.983442 6.985609 6.987773 6.989931 6.992084
6.994234 6.996383 6.998526 7.000664 7.002797
7.004928 7.007054 7.009173 7.011293 7.013413
7.015531 7.017644 7.019751 7.021854 7.023952
7.026047 7.028136 7.030221 7.032302 7.034377 7.03645
7.038516 7.040579 7.042638 7.044693 7.046752
7.048807 7.050857 7.052904 7.054947 7.056986
7.059022 7.061057 7.063088 7.065117 7.067143
7.069164 7.071185 7.073201 7.075212 7.07722 7.079223
7.081225 7.083223 7.085217 7.087209 7.089198
7.091181 7.09316 7.095133 7.097109 7.099078 7.101046
7.10301 7.104972 7.106931 7.108886 7.110838 7.112788
7.114738 7.116683 7.118623 7.120559 7.12249 7.124417
7.126341 7.128261 7.130178 7.132093 7.134005
7.135917 7.137825 7.139728 7.141627 7.143526
7.145421 7.147318 7.14921 7.151097 7.152981 7.15486
7.156735 7.158608 7.160476 7.162343 7.164213 7.16608
7.167944 7.169805 7.171665 7.173521 7.175375
7.177227 7.179074 7.180917 7.182757 7.184593
7.186426 7.188257 7.190082 7.191904 7.193725
7.195542 7.197355 7.199165 7.200971 7.202773
7.204572 7.206368 7.208162 7.209954 7.211743))
(RPAQQ KCKS
(.6931472 1.745279 3.210475 4.970805 7.086461 9.387441 11.9216
14.58973 17.4321 20.47031 23.60164 26.88869 30.2837
33.74855 37.30569 40.9732 44.74168 48.56186 52.47098
56.44447 60.4607 64.55229 68.69864 72.91252 77.20435
81.54286 85.91288 90.32599 94.76786 99.24979
103.8275 108.4415 113.1009 117.7841 122.529 127.2961
132.1028 136.9478 141.8214 146.7312 151.6759 156.639
161.6505 166.6793 171.7323 176.8016 181.922 187.0912
192.2819 197.4874 202.7136 207.9662 213.2325 218.536
223.8641 229.2163 234.5921 239.9802 245.3911 250.819
256.2584 261.7298 267.2418 272.7696 278.308 283.8616
289.4531 295.0636 300.7014 306.349 312.0105 317.6898
323.3907 329.1088 334.8439 340.5917 346.356 352.1403
357.9368 363.7528 369.5914 375.4382 381.307 387.1836
393.0749 398.9771 404.8937 410.8276 416.7722
422.7239 428.6859 434.671 440.6725 446.6839 452.7113
458.7484 464.798 470.869 476.9464 483.0531 489.1717
495.3075 501.4549 507.6138 513.7786 519.9546 526.147
532.3503 538.5645 544.7843 551.0147 557.2557
563.5047 569.7589 576.0309 582.3179 588.6101
594.9098 601.2194 607.5388 613.8631 620.2041
626.5522 632.9098 639.2789 645.6618 652.0561
658.4637 664.8824 671.31 677.7463 684.1893 690.6429
697.1051 703.5738 710.0529 716.5383 723.0401 729.554
736.0818 742.6138 749.1576 755.7054 762.2592 768.817
775.3863 781.9707 788.5608 795.1548 801.7545
808.3689 814.9888 821.6125 828.2416 834.8904
841.5445 848.2074 854.8808 861.5629 868.2502
874.9443 881.6453 888.3597 895.0791 901.8053 908.538
915.2789 922.0264 928.7851 935.5487 942.3187
949.0919 955.8746 962.6604 969.4526 976.2539
983.0585 989.8721 996.6889 1003.512 1010.349
1017.192 1024.037 1030.887 1037.742 1044.604
1051.472 1058.347 1065.227 1072.124 1079.024
1085.932 1092.848 1099.771 1106.7 1113.635 1120.576
1127.527 1134.481 1141.441 1148.407 1155.375
1162.348 1169.33 1176.321 1183.323 1190.329 1197.338
1204.353 1211.37 1218.392 1225.417 1232.445 1239.477
1246.518 1253.561 1260.609 1267.679 1274.753
1281.832 1288.917 1296.014 1303.118 1310.23 1317.347
1324.465 1331.588 1338.714 1345.847 1352.982
1360.121 1367.263 1374.413 1381.57 1388.729 1395.892
1403.057 1410.224 1417.397 1424.577 1431.764
1438.957 1446.157 1453.361 1460.569 1467.78 1474.997
1482.217 1489.442 1496.671 1503.907 1511.147 1518.39
1525.636 1532.885 1540.137 1547.392 1554.651
1561.915 1569.191 1576.47 1583.753 1591.037 1598.334
1605.634 1612.936 1620.243 1627.557 1634.873
1642.195 1649.521 1656.851 1664.185 1671.523 1678.87
1686.22 1693.573 1700.928 1708.29 1715.656 1723.029
1730.407 1737.793 1745.185 1752.581 1759.98 1767.381
1774.784 1782.189 1789.599 1797.015 1804.434
1811.857 1819.289 1826.722 1834.163 1841.605
1849.058 1856.514 1863.974 1871.437 1878.903 1886.37
1893.84 1901.314 1908.791 1916.273 1923.757 1931.245
1938.74 1946.24 1953.743 1961.251 1968.761 1976.273
1983.787 1991.306 1998.83 2006.355 2013.888 2021.422
2028.959 2036.498 2044.039 2051.585 2059.134
2066.691 2074.257 2081.826 2089.398 2096.974
2104.556 2112.139 2119.725 2127.315 2134.911
2142.508 2150.108 2157.711 2165.317 2172.926
2180.537 2188.153 2195.771 2203.397 2211.026
2218.656 2226.289 2233.924 2241.562 2249.206
2256.852 2264.5 2272.15 2279.802 2287.457 2295.114
2302.776 2310.441 2318.108 2325.781 2333.456
2341.133 2348.815 2356.501 2364.189 2371.879
2379.578 2387.284 2394.994 2402.707 2410.422 2418.14
2425.859 2433.58 2441.31 2449.043 2456.778 2464.519
2472.263 2480.008 2487.758 2495.513 2503.272
2511.032 2518.794 2526.559 2534.327 2542.096
2549.868 2557.641 2565.416 2573.193 2580.973
2588.755 2596.539 2604.324 2612.114 2619.904
2627.698 2635.495 2643.294 2651.098 2658.905
2666.716 2674.529 2682.343 2690.16 2697.978 2705.801
2713.629 2721.458 2729.29 2737.124 2744.961 2752.8
2760.644 2768.491 2776.342 2784.195 2792.05 2799.908
2807.769 2815.635 2823.504 2831.376 2839.249
2847.125 2855.002 2862.887 2870.774 2878.663
2886.556 2894.45 2902.348 2910.248 2918.151 2926.057
2933.966 2941.878 2949.792 2957.708 2965.63 2973.555
2981.481 2989.412 2997.351 3005.291 3013.231
3021.176 3029.123 3037.071 3045.023 3052.977
3060.933 3068.891 3076.851 3084.818 3092.786
3100.755 3108.725 3116.699 3124.68 3132.663 3140.647
3148.633 3156.621 3164.611 3172.603 3180.596
3188.592 3196.59 3204.591 3212.593 3220.598 3228.604
3236.614 3244.626 3252.642 3260.659 3268.682 3276.71
3284.739 3292.771 3300.803 3308.836 3316.871
3324.911 3332.954 3341.0 3349.047 3357.098 3365.149
3373.202 3381.257 3389.313 3397.37 3405.431 3413.492
3421.557 3429.624 3437.692 3445.763 3453.838
3461.914 3469.992 3478.072 3486.154 3494.237
3502.323 3510.413 3518.505 3526.599 3534.694
3542.793 3550.893 3558.995 3567.099 3575.205
3583.314 3591.425 3599.537 3607.655 3615.774
3623.895 3632.017 3640.144 3648.272 3656.401
3664.535 3672.67 3680.807 3688.948 3697.09 3705.232
3713.378 3721.527 3729.677 3737.829 3745.985
3754.143 3762.302 3770.463 3778.624 3786.787
3794.951 3803.118 3811.286 3819.459 3827.637
3835.818 3843.999 3852.182 3860.367 3868.553
3876.739 3884.928 3893.121 3901.316 3909.511
3917.711 3925.912 3934.116 3942.321 3950.527
3958.736 3966.949 3975.163 3983.378 3991.594
3999.814 4008.035 4016.256 4024.482 4032.713
4040.946 4049.181 4057.416 4065.654 4073.892
4082.133 4090.375 4098.619 4106.865 4115.111
4123.359 4131.609 4139.861 4148.114 4156.369 4164.63
4172.894 4181.158 4189.425 4197.694 4205.964
4214.236 4222.512 4230.79 4239.07 4247.353 4255.637
4263.925 4272.213 4280.504 4288.795 4297.088
4305.385 4313.682 4321.982 4330.285 4338.589
4346.894 4355.2 4363.507 4371.819 4380.131 4388.446
4396.763 4405.083 4413.404 4421.727 4430.052 4438.38
4446.711 4455.043 4463.377 4471.711 4480.046
4488.383 4496.721 4505.061 4513.403 4521.747
4530.093 4538.443 4546.794 4555.146 4563.5 4571.856
4580.215 4588.578 4596.942 4605.307 4613.672 4622.04
4630.407 4638.778 4647.149 4655.523 4663.903
4672.284 4680.667 4689.052 4697.441 4705.83 4714.222
4722.615 4731.01 4739.405 4747.802 4756.201 4764.601
4773.002 4781.405 4789.808 4798.214 4806.622
4815.031 4823.441 4831.852 4840.263 4848.677
4857.092 4865.509 4873.929 4882.35))
(RPAQQ EKCKS
(2.0 5.727501 24.79086 144.1429 1195.669 11937.51 150481.9
2.168894E6 3.721026E7 7.765049E8 1.778525E10 4.760038E11
1.419204E13 4.537425E14 1.59094E16 6.229257E17
2.698138E19 1.230691E21 6.135578E22 3.262281E24
1.810294E26 1.083192E28 6.846026E29 4.629193E31
3.383949E33 2.591873E35 2.048749E37))
(RPAQQ PPRODS
(2.0 6.0 30.0 210.0 2310.0 30030.0 510510.0 9.69969E6
2.230929E8 6.469693E9 2.005605E11 7.420738E12 3.042503E14
1.308276E16 6.148898E17 3.258916E19 1.92276E21
1.172884E23 7.858322E24 5.579408E26 4.072968E28
3.217645E30 2.670645E32 2.376874E34 2.305568E36))
(RPAQQ EXPLAIN
((ISPRIME IS A PREDICATE WHICH TESTS IF A NUMBER IS PRIME)
(PRIMES IS A LIST OF THE FIRST 677 PRIME NUMBERS)
(LOGS IS A LIST OF THE LOGS OF THE FIRST 677 PRIMES)
(PRODLOGS IS A LIST OF THE PRODUCTS OF THE LOGS OF THE FIRST
K PRIMES, EACH ENTRY IN PRODLOGS REPRESENTS A
LARGER K THAN THE PRECEDING ONE)
(LOGLOGS IS, FOR EACH K, LOG (LOG (KTH PRIME)))
(SUMLOGLOGS IS, FOR EACH K, THE SUM OF THE FIRST K MEMBERS OF
LOGLOGS; I.E., THE SUM OF THE LOG OF THE LOG THE
ITH PRIME, FOR I FROM 1 TO K)
(LOGCKS IS, FOR EACH K, THE LOG OF C-SUB-K, AND IS DEFINED AS
LOG (CK)
=
(1/K)
(LOGLOG (P1)
+ LOGLOG (P2)
+ LOGLOG (P3)
+... + LOGLOG (PK)))
(CKS IS ANTILOG (LOGCKS)
; CKS (K)
= KTH-ROOT OF THE PRODUCT
(FOR I FROM 1 TO K)
OF LOG (ITH PRIME))
(KCKS IS, FOR EACH K, K TIMES CK)
(EKCKS IS, FOR EACH K, E TO THE (K TIMES CK)
; THAT IS, ANTILOG (KCKS))
(N (K,T)
= ANTILOG (K CK KTH-ROOT (T))
; I.E., N (K,T)
= EKCK TIMES ANTILOG (KTH-ROOT (T)))
(MIN OF A LIST RETURNS (I V)
, WHERE I IS THE POSITION OF THE MINIMUN ELEMENT AND V
IS THAT ELEMENT)
(NOFT (T)
COMPUTES THE VALUES N (K,T)
FOR VARIOUS K'S, AND PICKS THE MINIMAL ONE OF THESE. IT
RETURNS A LIST OF THE FORM (N-VALUE MINIMIZING-K))
(PPRODS (N)
IS THE PRODUCT OF THE FIRST N PRIMES)
(SUMLOGS (N)
IS THE SUM OF THE LOGS OF THE FIRST N PRIMES)
(AM1 (K,T)
COMPUTES THE (ALPHA-SUB-I - 1)
VALUES FOR I FROM 1 TO K, THAT IS, THE POWERS OF THE
EACH OF THE FIRST K PRIMES IN N)
(TABLE (T1 T2)
PRINTS, FOR EACH T FROM T1 TO T2, T, THE OPTIMAL N,
THE OPTIMAL K (THE ONE WHICH GIVES THIS N)
, AND THE OPTIMAL AHPHA-MINUS-1'S WHICH FORM THE
EXPONENTS OF THE PRIMES AND GENERATE THIS N)
(AKM1 (K,T)
JUST GIVES ALPHA-1 FOR THE FINAL (KTH)
PRIME FACTOR OF N)
(LOGQUO (K)
IS LOG (PRIME (K-1))
/LOG
(PRIME (K)))
(CUT IS A FUNCTION WHICH DETERMINES WHETHER THE EXPONENT OF
THE KTH PRIME FACTOR IS TOO SMALL. CURRENTLY, WE USE
LOGQUO TO ENSURE THAT PRIME (K)
**AKM1 IS AT LEAST AS BIG AS PRIME (K-1))
(IDEAL (I)
IS THE MINIMUM N WHICH CAN HOPE TO HAVE I DIVISORS)
(UNFAC TAKES A LIST OF ALPHA-MINUS-1S AND GIVES BACK THE CORR
N)
(ROUND (X)
ROUNDS X UP OR DOWN TO THE NEAREST INTEGER)))
(RPAQQ SUMLOGS
(.6931472 1.791759 3.401197 5.347107 7.745002 10.30995
13.14316 16.0876 19.2231 22.59039 26.02438 29.6353
33.34887 37.11007 40.96022 44.93051 49.00805
53.11892 57.32361 61.58629 65.87675 70.2462 74.66504
79.15367 83.72838 88.3435 92.97823 97.65106 102.3424
107.0698 111.914 116.7892 121.7092 126.6436 131.6476
136.6649 141.7211 146.8149 151.9328 157.0861
162.2735 167.472 172.7243 177.987 183.2702 188.5635
193.9153 199.3225 204.7475 210.1812 215.6322
221.1087 226.5935 232.1189 237.668 243.2402 248.8349
254.437 260.061 265.6994 271.3448 277.025 282.7518
288.4916 294.2378 299.9967 305.7988 311.6189
317.4682 323.3233 329.1898 335.0731 340.9784 346.9
352.8376 358.7856 364.7492 370.7331 376.7271
382.7408 388.7786 394.8213 400.8874 406.9581
413.0426 419.1362 425.2432 431.3679 437.5013 443.639
449.7853 455.957 462.1453 468.3417 474.5543 480.7749
487.0074 493.2631 499.5227 505.8161 512.1206
518.4431 524.7764 531.1203 537.4677 543.8255
550.2005 556.5857 562.981 569.3796 575.7881 582.2064
588.6313 595.0594 601.5067 607.9697 614.4359
620.9082 627.3898 633.8805 640.3743 646.886 653.4037
659.9302 666.4683 673.0208 679.5847 686.1625
692.7514 699.3486 705.9539 712.5646 719.186 725.8153
732.45 739.0951 745.7453 752.4136 759.0944 765.7902
772.4885 779.199 785.9119 792.6297 799.35 806.0822
812.8309 819.5844 826.3401 833.1005 839.877 846.6581
853.4414 860.2292 867.0394 873.8539 880.6772
887.5113 894.354 901.2009 908.0542 914.9138 921.788
928.6663 935.5508 942.4414 949.3401 956.2449
963.1616 970.0823 977.0088 983.9374 990.8757
997.8159 1004.762 1011.717 1018.675 1025.642
1032.611 1039.585 1046.576 1053.571 1060.568
1067.568 1074.574 1081.585 1088.604 1095.627
1102.656 1109.705 1116.755 1123.814 1130.879
1137.953 1145.033 1152.117 1159.208 1166.309
1173.413 1180.522 1187.636 1194.751 1201.872
1209.002 1216.14 1223.292 1230.446 1237.603 1244.765
1251.928 1259.095 1266.266 1273.439 1280.614
1287.799 1294.985 1302.176 1309.392 1316.612
1323.837 1331.067 1338.311 1345.561 1352.822
1360.085 1367.35 1374.618 1381.889 1389.166 1396.446
1403.728 1411.013 1418.307 1425.607 1432.909
1440.214 1447.52 1454.828 1462.141 1469.461 1476.79
1484.123 1491.465 1498.81 1506.158 1513.51 1520.867
1528.226 1535.591 1542.958 1550.334 1557.712
1565.094 1572.478 1579.863 1587.253 1594.644
1602.038 1609.439 1616.852 1624.268 1631.687
1639.107 1646.541 1653.978 1661.415 1668.859 1676.31
1683.762 1691.219 1698.681 1706.147 1713.616
1721.089 1728.571 1736.057 1743.546 1751.035
1758.531 1766.033 1773.541 1781.054 1788.575
1796.104 1803.636 1811.17 1818.705 1826.243 1833.781
1841.325 1848.875 1856.428 1863.985 1871.551
1879.117 1886.692 1894.269 1901.856 1909.446
1917.041 1924.638 1932.237 1939.838 1947.44 1955.047
1962.656 1970.27 1977.885 1985.506 1993.133 2000.765
2008.399 2016.04 2023.682 2031.325 2038.97 2046.619
2054.274 2061.929 2069.593 2077.257 2084.924
2092.593 2100.263 2107.938 2115.616 2123.303 2131.0
2138.7 2146.402 2154.108 2161.82 2169.534 2177.25
2184.969 2192.695 2200.422 2208.151 2215.883
2223.618 2231.356 2239.095 2246.84 2254.585 2262.34
2270.098 2277.856 2285.617 2293.379 2301.145
2308.916 2316.689 2324.464 2332.241 2340.019
2347.799 2355.582 2363.37 2371.16 2378.953 2386.752
2394.552 2402.354 2410.162 2417.973 2425.786
2433.601 2441.426 2449.258 2457.095 2464.934
2472.775 2480.619 2488.463 2496.309 2504.165
2512.024 2519.885 2527.752 2535.621 2543.493
2551.368 2559.25 2567.135 2575.02 2582.908 2590.798
2598.69 2606.585 2614.481 2622.378 2630.276 2638.177
2646.081 2653.986 2661.891 2669.799 2677.711
2685.623 2693.54 2701.459 2709.379 2717.304 2725.234
2733.167 2741.101 2749.037 2756.975 2764.914
2772.858 2780.807 2788.757 2796.71 2804.665 2812.623
2820.582 2828.547 2836.515 2844.486 2852.46 2860.435
2868.414 2876.395 2884.381 2892.372 2900.364
2908.358 2916.354 2924.35 2932.356 2940.363 2948.373
2956.386 2964.4 2972.418 2980.438 2988.461 2996.487
3004.516 3012.548 3020.582 3028.617 3036.659
3044.704 3052.75 3060.801 3068.861 3076.921 3084.982
3093.047 3101.114 3109.182 3117.254 3125.328
3133.404 3141.481 3149.561 3157.648 3165.735
3173.824 3181.913 3190.006 3198.107 3206.209
3214.313 3222.418 3230.526 3238.634 3246.745
3254.856 3262.971 3271.086 3279.206 3287.326
3295.449 3303.572 3311.7 3319.829 3327.963 3336.098
3344.239 3352.385 3360.533 3368.683 3376.833
3384.984 3393.135 3401.293 3409.453 3417.617
3425.782 3433.95 3442.119 3450.289 3458.461 3466.633
3474.807 3482.983 3491.161 3499.341 3507.525
3515.708 3523.895 3532.086 3540.278 3548.471
3556.667 3564.864 3573.063 3581.263 3589.468
3597.676 3605.885 3614.095 3622.309 3630.524 3638.74
3646.959 3655.18 3663.403 3671.628 3679.855 3688.087
3696.321 3704.556 3712.793 3721.034 3729.276
3737.519 3745.768 3754.016 3762.268 3770.523
3778.779 3787.035 3795.295 3803.557 3811.821
3820.087 3828.358 3836.629 3844.902 3853.176 3861.45
3869.727 3878.003 3886.283 3894.564 3902.849
3911.141 3919.435 3927.73 3936.025 3944.323 3952.621
3960.921 3969.221 3977.528 3985.834 3994.143
4002.455 4010.768 4019.085 4027.402 4035.72 4044.042
4052.367 4060.693 4069.02 4077.348 4085.679 4094.012
4102.345 4110.682 4119.025 4127.371 4135.717
4144.065 4152.414 4160.765 4169.117 4177.47 4185.826
4194.182 4202.539 4210.899 4219.259 4227.621
4235.985 4244.351 4252.724 4261.098 4269.474
4277.851 4286.231 4294.612 4302.995 4311.382
4319.771 4328.162 4336.556 4344.951 4353.35 4361.75
4370.15 4378.553 4386.956 4395.364 4403.772 4412.182
4420.595 4429.01 4437.426 4445.842 4454.258 4462.681
4471.103 4479.529 4487.955 4496.385 4504.817 4513.25
4521.685 4530.123 4538.565 4547.007 4555.45 4563.894
4572.339 4580.785 4589.233 4597.682 4606.133
4614.586 4623.042 4631.502 4639.962 4648.424
4656.886 4665.352 4673.82 4682.293 4690.766 4699.24
4707.715 4716.191 4724.668 4733.147 4741.627
4750.109 4758.598 4767.089 4775.582 4784.076
4792.574 4801.073 4809.574 4818.077 4826.581
4835.085 4843.591 4852.098 4860.607 4869.117
4877.628 4886.14 4894.654 4903.17 4911.687 4920.205
4928.724 4937.243 4945.765 4954.286 4962.811
4971.338 4979.867))
(RPAQQ CUT .5)
(RPAQQ GLOBALVARS (CUT))
(RPAQQ LOGQUO
(0.0 .6309299 .682606 .8270876 .8115076 .9348704 .9053146
.9622251 .939067 .9311608 .9805791 .9510011 .9723571
.987337 .9768975 .9697393 .9736986 .9918905 .9776871
.9863966 .9935254 .9819224 .9888222 .9844507 .9811846
.9912442 .9957691 .9918465 .9960525 .9923763 .9758888
.9936392 .9908975 .9970629 .9861166 .9973424 .9922935
.9926372 .995263 .9931504 .9934275 .9978626 .9897614
.9980206 .9961171 .9980917 .9890593 .9897702 .9967229
.9983856 .9968234 .9953574 .9984805 .9926421 .9957429
.9958583 .9959681 .9986776 .9961063 .997457 .9987438
.9938865 .9918498 .9977447 .9988845 .9977949 .9925517
.9969133 .9950008 .9990185 .9980574 .9971353 .9962678
.9972615 .9973123 .9982349 .9973935 .996598 .9983275
.9967152 .9959993 .9992119 .9961301 .9992373 .9977383
.9985114 .9977971 .9971166 .9985791 .9992947 .9986005
.995889 .9973235 .9986799 .9973985 .9987165 .9980974
.9962751 .999388 .9946233 .9982504 .9971347 .9983081
.9983291 .9994472 .9983559 .9973046 .9984074 .9984257
.9994791 .9984499 .9984675 .9989877 .9994966 .9970219
.9975672 .9995181 .9990419 .9985758 .9985909 .9995332
.9972372 .9990908 .998648 .9982189 .9978072 .9982713
.9978707 .9983207 .998754 .9987658 .9991834 .9983825
.9987997 .9992057 .9984262 .9992199 .9973083 .99811
.9977681 .9996314 .9981738 .9996376 .9992782 .9996406
.9982189 .997548 .9993072 .999655 .9993128 .9976253
.9993289 .9996658 .9993341 .9967259 .9993542 .9987186
.9984163 .998747 .9993778 .9990726 .9990792 .9978786
.9993999 .9991051 .9991115 .998825 .9991258 .9982703
.9994284 .9991473 .999717 .9985953 .9997207 .9991661
.9986228 .9997263 .9986407 .9997298 .9991929 .9976116
.9994749 .9997383 .9994782 .9992214 .9992262 .9989758
.9992373 .999242 .9972619 .9997538 .9987766 .9990298
.9987979 .9992842 .9992883 .9990574 .9985999 .9995366
.9993082 .9993121 .9997715 .9993172 .998646 .9988827
.9980152 .9997812 .9995638 .9993485 .9997836 .9993531
.9995706 .9997857 .9995728 .998728 .9997892 .9993697
.996494 .9993908 .9993939 .9991965 .9982122 .9990177
.9986381 .9996135 .9998073 .9996154 .9994253 .9992382
.9996209 .9998107 .9994345 .9988768 .999072 .9998152
.9996312 .999816 .9996329 .9994516 .9989107 .9989206
.9992856 .9989364 .9994716 .999649 .9994755 .9993043
.9996535 .9993103 .9996566 .9988062 .9996609 .9994934
.9998315 .9996638 .9994975 .9998329 .9995004 .999172
.9983619 .9995127 .9996761 .9998384 .9980796 .9996826
.9998416 .9992115 .9990609 .9998442 .999224 .9993827
.9995392 .9995409 .9995427 .9986394 .9995497 .9997009
.9998506 .9991082 .9992619 .9991203 .9994172 .9988431
.9989971 .9995726 .999716 .9998581 .999717 .9998587
.9992964 .9991613 .9995828 .9995842 .9987622 .9998632
.9989117 .9998647 .9985221 .9995999 .9994688 .9996031
.9997362 .9998683 .999737 .999476 .9996085 .9993504
.9998705 .9993547 .9991029 .9993633 .9996195 .9992431
.9998744 .9997489 .9998747 .9993758 .9992552 .9998763
.9990156 .9998775 .9996334 .9997562 .9998782 .9993934
.9995169 .9989209 .998577 .9997644 .9996475 .9995316
.9990693 .9998841 .9997688 .9995387 .9990833 .999886
.999772 .9995457 .9996604 .9996614 .9997748 .9993271
.9998882 .9987783 .9996688 .9998899 .9996701 .9997806
.9996717 .9992379 .9996749 .9997837 .9998921 .9996767
.999785 .9996783 .9993593 .999681 .9996818 .9992613
.9997898 .9996854 .9993734 .9995842 .9996891 .9997932
.9986656 .9990851 .9994948 .9995974 .9997993 .9996996
.9998999 .9997006 .9989094 .9994094 .9999018 .9992181
.9996109 .999806 .99942 .9993271 .9995217 .9999046
.9998093 .9996199 .9997157 .9997164 .9998113 .9999058
.9998119 .9997182 .9996256 .9998132 .9999068 .9997207
.999536 .9999074 .9995383 .999632 .9998164 .9993599
.9995451 .9994565 .9999096 .9997293 .99982 .9999102
.9992835 .9993768 .9998225 .9997343 .9996468 .9997358
.9998242 .9992126 .9996517 .9995662 .9997405 .9997411
.9996558 .9995713 .9994876 .9994053 .9998307 .9997463
.9997471 .9999157 .9988284 .9999167 .9995848 .9996688
.9998348 .9994238 .9998358 .9996726 .9995106 .9997561
.9995138 .9998384 .9997579 .9991976 .9996007 .9999203
.9993649 .9989758 .9998432 .9999217 .9995313 .9997664
.9998446 .9995349 .9997681 .9996917 .9998462 .9996929
.9991604 .999924 .999848 .9999241 .9995459 .9989478
.9999252 .9997759 .9997764 .9997768 .9998515 .9997776
.9999259 .9995568 .9998526 .9995593 .9999266 .9996343
.999927 .9994178 .9999274 .9994213 .9997837 .9992823
.9994293 .9997156 .999858 .9999292 .9998583 .9999292
.9992252 .9997195 .9995806 .9997908 .9996524 .9999306
.9998613 .9997924 .9999309 .9997929 .9996556 .9999313
.9995885 .9996583 .9999317 .9996596 .9995252 .9997971
.999865 .9997977 .999731 .9997986 .9997989 .9994659
.9996011 .9999336 .9998675 .9995372 .9998023 .9998684
.9997372 .9996726 .9997387 .9998045 .9998048 .9992873
.9998064 .9999355 .9996783 .9995514 .9998721 .9998084
.9994275 .9999365 .9996834 .9995583 .9998741 .9999371
.9996862 .9995621 .9998752 .9997509 .9994416 .9998763
.9998147 .9999382 .9998767 .9998154 .9999385 .9996319
.9998775 .99939 .9993329 .9996378 .9999398 .9998796
.9998197 .99982 .99994 .9998204 .9993441 .9999405
.9998218 .9995265 .9998229 .9996467 .9999413 .9998239
.9996486 .9995335 .9999419 .9998836 .9998259 .9995947
.9998844 .9999423 .9994821 .9993132 .9997152 .9998294
.9999432 .9997164 .9999433 .9997175 .9999435 .9997183
.9998313 .9999439 .9997196 .999944 .9997204 .9998326
.9997773 .999169 .9997244 .999945 .9997252 .9997807
.9998358 .999727 .9995102 .9998372 .9996753 .9996762
.9999462 .9995163 .9998393 .999893 .9998397 .9998399
.9995213 .9999468 .9997351 .9996302 .9998419 .9998947
.9999474 .9998948 .9993717 .9999478 .9996874 .9998439
.9995852 .9997932 .9998451 .9998453 .9995376 .9995905
.9999489 .9998979 .9998471 .9999491 .9998473 .9998476
.9997465 .9998481 .999697 .9996978 .9995484 .99995
.9998499 .9999001 .9995516 .9998012 .9994063 .9999013
.9999507 .9999015 .9998524 .9999509 .9997055 .999902
.9996579 .9992708 .9997579 .9998552 .9997106 .9996635
.9998561 .9997606 .9997134 .9999522 .9999048 .9998572
.9998099 .9998577 .9997632 .9999526 .9999055 .9996697
.9998588 .999859 .9999061 .9998594 .9999531 .9997661
.9999532 .999627 .9997211 .9998144))
(RPAQQ MINN
(0 2 4 6 16 12 64 24 36 48 0 60 0 192 144 120 0 180 0 240 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0))
(RPAQQ IDEAL ((1.0 1)
(2.0 1)
(4.0 1)
(5.467377 2)
(8.25487 2)
(11.98054 2)
(16.87469 2)
(23.21121 2)
(31.31439 2)
(41.56663 2)
(54.41699 2)
(51.88116 3)
(63.28853 3)
(76.43985 3)
(91.5161 3)
(108.711 3)
(128.2316 3)
(150.2991 3)
(175.1494 3)
(203.0338 3)
(234.2197 3)
(268.9915 3)
(307.6512 3)
(350.5191 3)
(397.9349 3)
(450.2587 3)
(507.8711 3)
(571.1749 3)
(640.596 3)
(716.5838 3)
(591.1437 4)
(649.0607 4)
(711.1102 4)
(777.4945 4)
(848.4221 4)
(924.1077 4)
(1004.773 4)
(1090.646 4)
(1181.962 4)
(1278.964 4)
(1381.899 4)
(1491.026 4)
(1606.607 4)
(1728.914 4)
(1858.226 4)
(1994.83 4)
(2139.02 4)
(2291.1 4)
(2451.38 4)
(2620.181 4)
(2797.829 4)
(2984.662 4)
(3181.026 4)
(3387.274 4)
(3603.77 4)
(3830.887 4)
(4069.009 4)
(4318.525 4)
(4579.837 4)
(4853.362 4)
(5139.514 4)
(5438.729 4)
(5751.452 4)
(6078.13 4)
(6419.229 4)
(6775.228 4)
(7146.609 4)
(7533.869 4)
(7937.521 4)
(8358.08 4)
(8796.082 4)
(9252.066 4)
(9726.597 4)
(10220.24 4)
(10733.57 4)
(11267.19 4)
(11821.71 4)
(12397.74 4)
(12995.92 4)
(13616.9 4)
(14261.34 4)
(14929.91 4)
(15623.3 4)
(16342.23 4)
(17087.41 4)
(17859.56 4)
(18659.45 4)
(19487.83 4)
(20345.48 4)
(21233.2 4)
(22151.81 4)
(23102.12 4)
(24084.98 4)
(25101.27 4)
(26151.83 4)
(27237.59 4)
(28359.45 4)
(29518.33 4)
(30715.18 4)
(31950.98 4)
(33226.71 4)
(34543.36 4)
(35901.98 4)
(37303.57 4)
(38749.23 4)
(28682.37 5)
(29669.95 5)
(30683.78 5)
(31724.39 5)
(32792.3 5)
(33888.01 5)
(35012.08 5)
(36165.04 5)
(37347.42 5)
(38559.78 5)
(39802.69 5)
(41076.7 5)
(42382.38 5)
(43720.33 5)
(45091.13 5)
(46495.37 5)
(47933.63 5)
(49406.57 5)
(50914.75 5)
(52458.86 5)
(54039.48 5)
(55657.25 5)
(57312.87 5)
(59006.92 5)
(60740.12 5)
(62513.12 5)
(64326.64 5)
(66181.28 5)
(68077.84 5)
(70016.92 5)
(71999.34 5)
(74025.71 5)
(76096.86 5)
(78213.47 5)
(80376.28 5)
(82586.04 5)
(84843.58 5)
(87149.6 5)
(89504.91 5)
(91910.3 5)
(94366.58 5)
(96874.52 5)
(99434.9 5)
(102048.7 5)
(104716.6 5)
(107439.5 5)
(110218.3 5)
(113053.7 5)
(115946.8 5)
(118898.3 5)
(121909.2 5)
(124980.3 5)
(128112.6 5)
(131307.0 5)
(134564.4 5)
(137885.8 5)
(141272.1 5)
(144724.2 5)
(148243.1 5)
(151829.9 5)
(155485.5 5)
(159210.8 5)
(163007.0 5)
(166875.1 5)
(170815.9 5)
(174830.7 5)
(178920.5 5)
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(RPAQQ FIXEDNS
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30)
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48)
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60)
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(DECLARE: DONTCOPY
(FILEMAP (NIL (526 4270 (ISPRIME 538 . 642) (LOGN 646 . 773) (N 777
. 890) (MIN 894 . 1128) (NOFT 1132 . 1466) (AM1 1470 . 1693) (TABLE
1697 . 2341) (AKM1 2345 . 2514) (CUT 2518 . 2606) (GETMINN 2610 .
2783) (TAU 2787 . 2875) (FAC1 2879 . 3112) (FACS 3116 . 3207) (UNFAC
3211 . 3348) (ROUND 3352 . 3397) (TAU1 3401 . 3518) (QTABLE 3522 .
4267)))))
STOP