On a curious biconditional involving the divisors of odd perfect numbers

Jose Arnaldo B. Dris
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 4, Pages 1–13
Full paper (PDF, 177 Kb)

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Authors and affiliations

Jose Arnaldo B. Dris
University of the Philippines-Diliman

Abstract

We investigate the implications of a curious biconditional involving the divisors of odd perfect numbers, if Dris conjecture that q^k < n holds, where q^kn² 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.

Keywords

• Odd perfect number
• Abundancy index
• Deficiency

AMS Classification

• 11A25

References

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