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C00003 00003	.COMMENT AM Conjec
C00005 00004	.COMMENT OVERLAY Complete the Square
C00006 ENDMK
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.COMMENT AM Conjec;
.ONCE CENTER SELECT 2
↓_Maximally Divisible Numbers_↓

.BEGIN SELECT 7 INDENT 0 PREFACE 0 TURN ON "_∞→\↑↓[]{}&" SELECT 2 TABS 60

⊗2Max-divis(n) =⊗4↓d↓f⊗* (∀m<n) d(m) < d(n)

↓_CONJECTURE:_↓   IF   n = ↓2↑a⊗71⊗*↓3↑a⊗72⊗*↓5↑a⊗73⊗*...p⊗7↓k⊗*↑a⊗7k⊗*

⊗2where   p↓i  is  the  i↑t↑h  prime, 

and   (a↓i + 1) / (a↓j + 1)   "="   log(p↓j ) / log(p↓i)

THEN   Max-divis(n).
↓_∞ →\_↓                                          

For example:   n could be

2⊗7↑8⊗*3⊗7↑5⊗*5⊗7↑3⊗*7⊗7↑2⊗*11⊗7↑2⊗*13⊗7↑1⊗*17⊗7↑1⊗*19⊗7↑1⊗*23⊗7↑1⊗*29⊗7↑1⊗*31⊗7↑1⊗*37⊗7↑1⊗*41⊗7↑1⊗*43⊗7↑1⊗*47⊗7↑1⊗*53⊗7↑1⊗*
.SELECT 2

(a↓i + 1)'s  are  (9 6 4 3 3 2 2 2 2 2 2 2 2 2 2 2)

AM  Conjecture says that n is the smallest
integer with 3,981,312 divisors.
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.COMMENT OVERLAY Complete the Square;
.ONCE CENTER SELECT 2
↓__↓

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⊗4{A,B}, {U,V,W}⊗*\\\2, 3















{⊗4 {A,U}, {A,V}, {A,W},⊗*\\\ 6
 ⊗4  {B,U}, {B,V}, {B,W}⊗*⊗2 }⊗*
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