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# Odd Integers $N$ with Five Distinct Prime Factors for which $2 - 10^{-12} < \sigma(N)/N < 2 + 10^{-12}$

Masao Kishore
Mathematics of Computation
Vol. 32, No. 141 (Jan., 1978), pp. 303-309+s1-s12
DOI: 10.2307/2006281
Stable URL: http://www.jstor.org/stable/2006281
Page Count: 19
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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 $N |\sigma(N)/N - 2| > 10^{-14}$. 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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