Title: Upper Bounds for the Abundancy Indices I(n) and $I(n^2)$ where $N = {q^k}{n^2}$ is an Odd Perfect Number
Abstract: We investigate the implications of a curious biconditional involving divisors of odd perfect numbers, if Dris conjecture that $q^k < n$ holds, where $q^k n^2$ is an odd perfect number with Euler prime $q$. We then show that this biconditional holds unconditionally. Lastly, we prove that the inequality $q<n$ holds unconditionally.
Publication Year: 2013
Publication Date: 2013-09-04
Language: en
Type: article
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Cited By Count: 1
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