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arXiv · 2303.11974

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

Graeme Clayton·Cody S. Hansen
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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 $\frac{99}{37}\omega(N) - \frac{187}{37} \leq \Omega(N)$ and that if $3\nmid N$, then $\frac{51}{19}\omega(N)-\frac{46}{19} \leq \Omega(N)$.

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Graeme Clayton, Cody S. Hansen. 2023-03-21. On inequalities involving counts of the prime factors of an odd perfect number. https://arxiv.org/abs/2303.11974

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