Numbers whose positive divisors have small integral harmonic mean-Reference-Cited by-同舟云学术

Numbers whose positive divisors have small integral harmonic mean

Published:1997 Issue:218 Volume:66 Page:883-891
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Cohen G.

Abstract

A natural number n n is said to be harmonic when the harmonic mean H ( n ) H(n) of its positive divisors is an integer. These were first introduced almost fifty years ago. In this paper, all harmonic numbers less than 2 × 10 9 2\times 10^{9} are listed, along with some other useful tables, and all harmonic numbers n n with H ( n ) ≤ 13 H(n)\le 13 are determined.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1997-66-218/S0025-5718-97-00819-3/S0025-5718-97-00819-3.pdf

Reference9 articles.

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2. G. L. Cohen, Numbers whose positive divisors have small harmonic mean, Research Report R94-8 (June 1994), School of Mathematical Sciences, University of Technology, Sydney.

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4. Problem Books in Mathematics;Guy, Richard K.,1994

5. Outline of a proof that every odd perfect number has at least eight prime factors;Hagis, Peter, Jr.;Math. Comp.,1980

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