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.