From: kramsay@aol.commangled (Keith Ramsay)
Subject: Re: Questions Involving Number of Divisors
Date: 17 Jan 2000 05:04:08 GMT
Newsgroups: sci.math
Summary: [missing]

In article <pnnj18en56vu@forum.swarthmore.edu>, qqquet@hotbot.com (Leroy Quet)
writes:
|Let d(m) be the number of positive divisors of m.
|Are there a finite number of d(m) that are = m-n, for all fixed
|positive integers n?
|Are there a finite number of d(m) that are >=m/n, for all fixed
|positive integers n?
|The answer to both questions seems to be yes, but I have no proof.

Hardy and Wright, theorem 315: for every delta>0, d(m) is O(m^delta).
What you're trying to prove is just d(m)=o(m).

Keith Ramsay