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␈↓ d␈↓↓␈↓ β∀␈↓&Maximally Divisible Numbers␈↓)αβ


␈↓ d␈↓↓Max-divis(N) iff (∀m<n) d(m) < d(n)

␈↓ d␈↓↓     if  N  =  ␈↓#v2␈↓#␈↓#
a␈↓#␈↓ε1␈↓↓␈↓#v3␈↓#␈↓#
a␈↓#␈↓ε2␈↓↓␈↓#v5␈↓#␈↓#
a␈↓#␈↓ε3␈↓↓...p␈↓ε␈↓#vk␈↓#␈↓↓␈↓#
a␈↓#␈↓εk␈↓↓

␈↓ d␈↓↓where   p␈↓#vi␈↓#  is  the  i␈↓#
t␈↓#␈↓#
h␈↓#  prime,

␈↓ d␈↓↓and   (a␈↓#vi␈↓# + 1) / (a␈↓#vj␈↓# + 1)   "="   log(p␈↓#vj␈↓# ) / log(p␈↓#vi␈↓#)

␈↓ d␈↓↓**************************************************

␈↓ d␈↓↓For example:   n could be

␈↓ d␈↓↓2␈↓ε␈↓#
8␈↓#␈↓↓3␈↓ε␈↓#
5␈↓#␈↓↓5␈↓ε␈↓#
3␈↓#␈↓↓7␈↓ε␈↓#
2␈↓#␈↓↓11␈↓ε␈↓#
2␈↓#␈↓↓13␈↓ε␈↓#
1␈↓#␈↓↓17␈↓ε␈↓#
1␈↓#␈↓↓19␈↓ε␈↓#
1␈↓#␈↓↓23␈↓ε␈↓#
1␈↓#␈↓↓29␈↓ε␈↓#
1␈↓#␈↓↓31␈↓ε␈↓#
1␈↓#␈↓↓37␈↓ε␈↓#
1␈↓#␈↓↓41␈↓ε␈↓#
1␈↓#␈↓↓43␈↓ε␈↓#
1␈↓#␈↓↓47␈↓ε␈↓#
1␈↓#␈↓↓53␈↓ε␈↓#
1␈↓#␈↓↓
␈↓ d␈↓↓        (which equals 25,608,675,584).

␈↓ d␈↓↓(a␈↓#vi␈↓# + 1)'s  are  (9 6 4 3 3 2 2 2 2 2 2 2 2 2 2 2)

␈↓ d␈↓↓n has 3,981,312 divisors.


␈↓ d␈↓↓AM  Conjecture says that
␈↓ d␈↓↓n is the smallest integer with that many divisors.