On inequalities involving counts of the prime factors of an odd perfect number

arXiv2303.11974MaRDI QIDQ6430364

Cody S. Hansen, Graeme Clayton

Publication date: 21 March 2023

Abstract: Let $N$ be an odd perfect number. Let $omega(N)$ be the number of distinct prime factors of $N$ and let $Omega(N)$ be the total number (counting multiplicity) of prime factors of $N$. We prove that $frac9937omega(N)-frac18737leqOmega(N)$ and that if $3midN$, then $frac5119omega(N)-frac4619leqOmega(N)$.

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32) Factorization; primality (11A51)

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