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arXiv · 1103.1090

The Abundancy Index of Divisors of Odd Perfect Numbers

Jose Arnaldo B. Dris
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Abstract

If $N = {q^k}{n^2}$ is an odd perfect number, where $q$ is the Euler prime, then we show that $n < q$ is sufficient for Sorli's conjecture that $k = ν_{q}(N) = 1$ to hold. We also prove that $q^k < 2/3{n^2}$, and that $I(q^k) < I(n)$, where $I(x)$ is the abundancy index of $x$.

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Jose Arnaldo B. Dris. 2012-08-03. The Abundancy Index of Divisors of Odd Perfect Numbers. https://arxiv.org/abs/1103.1090

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