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Mathematics of Computation

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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
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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.


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Additional Information

G. L. Cohen
Affiliation: School of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia
Email: glc@maths.uts.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00819-3
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