Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Numbers whose positive divisors have small integral harmonic mean

Author: G. L. Cohen
Journal: Math. Comp. 66 (1997), 883-891
MSC (1991): Primary 11A25, 11Y70
MathSciNet review: 1397443
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11A25, 11Y70

Retrieve articles in all journals with MSC (1991): 11A25, 11Y70

Additional Information

G. L. Cohen
Affiliation: School of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia

Received by editor(s): July 7, 1994
Received by editor(s) in revised form: March 29, 1996
Dedicated: To Peter Hagis, Jr., on the occasion of his 70th birthday
Article copyright: © Copyright 1997 American Mathematical Society