From: Fred W. Helenius <fredh@ix.netcom.com>
Subject: Re: Q? max. possible divisors of N, as function of N
Date: Thu, 18 May 2000 05:42:11 -0400
Newsgroups: sci.math
Summary: [missing]

Star Dancing <stardancing1@mindspring.com> wrote:

>In number theory there was a (possibly obscure) unsolved problem
>as of some years ago:

>      What is the upper bound on the number of divisors, d(N) of a
>       number N, as a function of N?

>I have conjectured two possibilities, one of which is

>         d(N)max. ~ exp [ln(N) / lnln (N)]

See section 18.1 of Hardy & Wright, _An Introduction to the
Theory of Numbers_.  Theorem 317 states

lim sup  log d(n) log log n/log n = log 2.

Their notes say this was first proved in 1907.