Odd integers $N$ with five distinct prime factors for which $2-10^{-12}<\sigma (N)/N<2+10^{-12}$
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- by Masao Kishore PDF
- Math. Comp. 32 (1978), 303-309 Request permission
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 $2 < \sigma (N)/N < 2 + 2/{10^{10}}$.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 303-309
- MSC: Primary 10A20
- DOI: https://doi.org/10.1090/S0025-5718-1978-0485658-X
- MathSciNet review: 0485658