Note on the Odd Perfect Numbers

Frank Vega

doi:10.33774/coe-2022-3vgzg

Mathematics

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Note on the Odd Perfect Numbers

30 May 2022, Version 1

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Working Paper

Frank Vega

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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

The Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Under the assumption of the Riemann Hypothesis, we claim that there is not any odd perfect number at all.

Keywords

Riemann Hypothesis

Prime numbers

Odd perfect numbers

Superabundant numbers

Sum-of-divisors function

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