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.SELECT 1
.COMMENT AM Conjec;
.GROUP SKIP 4
.ONCE CENTER SELECT 2
↓_Maximally Divisible Numbers_↓

.BEGIN SELECT 7 INDENT 0 PREFACE 0 TURN ON "↑↓[]{}&" SELECT 2

⊗2Max-divis(N) iff (∀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
	(which equals 25,608,675,584).

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

n has 3,981,312 divisors.


AM  Conjecture says that
n is the smallest integer with that many divisors.
.END
.SKIP TO COLUMN 1