Note on the Odd Perfect Numbers

EasyChair Preprint no. 8121, version 1

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6 pagesDate: May 30, 2022

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.

Keyphrases: Odd perfect numbers, prime numbers, Riemann hypothesis, sum-of-divisors function, Superabundant numbers