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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unitary harmonic numbers


Authors: Peter Hagis and Graham Lord
Journal: Proc. Amer. Math. Soc. 51 (1975), 1-7
MSC: Primary 10A20
DOI: https://doi.org/10.1090/S0002-9939-1975-0369231-9
MathSciNet review: 0369231
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Abstract: If $ {d^ \ast }(n)$ and $ {\sigma ^ \ast }(n)$ denote the number and sum, respectively, of the unitary divisors of the natural number $ n$ then the harmonic mean of the unitary divisors of $ n$ is given by $ {H^ \ast }(n) = n{d^ \ast }(n)/{\sigma ^ \ast }(n)$. Here we investigate the properties of $ {H^ \ast }(n)$, and, in particular, study those numbers $ n$ for which $ {H^ \ast }(n)$ is an integer.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0369231-9
Article copyright: © Copyright 1975 American Mathematical Society