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Mathematics of Computation

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

 

 

Odd integers $ N$ with five distinct prime factors for which $ 2-10\sp{-12}<\sigma (N)/N<2+10\sp{-12}$


Author: Masao Kishore
Journal: Math. Comp. 32 (1978), 303-309
MSC: Primary 10A20
DOI: https://doi.org/10.1090/S0025-5718-1978-0485658-X
MathSciNet review: 0485658
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Abstract: We make a table of odd integers N with five distinct prime factors for which $ 2 - {10^{ - 12}} < \sigma (N)/N < 2 + {10^{ - 12}}$, and show that for such $ N\;\vert\sigma (N)/N - 2\vert > {10^{ - 14}}$. Using this inequality, we prove that there are no odd perfect numbers, no quasiperfect numbers and no odd almost perfect numbers with five distinct prime factors. We also make a table of odd primitive abundant numbers N with five distinct prime factors for which $ 2 < \sigma (N)/N < 2 + 2/{10^{10}}$.


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DOI: https://doi.org/10.1090/S0025-5718-1978-0485658-X
Article copyright: © Copyright 1978 American Mathematical Society