We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Infinitary harmonic numbers.
- Authors
Hagis, Peter; Cohen, Graeme L.
- Abstract
The infinitary divisors of a natural number n are the products of its divisors of the , where py is an exact prime-power divisor of n and (where yα = 0 or 1) is the binary representation of y. Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean. One of the results in this paper is that the number of infinitary harmonic numbers not exceeding x is less than 2.2 x1/2 2(1+ε)log x/log log x for any ε > 0 and x > n0(ε). A corollary is that the set of infinitary perfect numbers (numbers n whose proper infinitary divisors sum to n) has density zero.
- Publication
Bulletin of the Australian Mathematical Society, 1990, Vol 41, Issue 1, p151
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972700017949