From: Fred W. Helenius
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 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.