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arXiv · 1103.1437

A note on odd perfect numbers

Jose Arnaldo B. Dris·Florian Luca
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Abstract

In this note, we show that if $N$ is an odd perfect number and $q^{\alpha}$ is some prime power exactly dividing it, then $\sigma(N/q^{\alpha})/q^{\alpha}>5$. In general, we also show that if $\sigma(N/q^{\alpha})/q^{\alpha}<K$, where $K$ is any constant, then $N$ is bounded by some function depending on $K$.

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Jose Arnaldo B. Dris, Florian Luca. 2011-03-08. A note on odd perfect numbers. https://arxiv.org/abs/1103.1437

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