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arXiv · 2402.14234

The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number

Joshua Zelinsky
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Abstract

Write $T(n)$ as the sum of the reciprocals of the primes which divide $n$. Write $H(n) = \prod_{p|n}p/(p-1)$ where the product is over the prime divisors of $n$. We prove new bounds for $T(n)$ and $H(n)$ in terms of the smallest prime factor of $n$, under the assumption that $n$ is an odd perfect number. Some of the results also apply under the weaker assumption that $n$ is odd and primitive non-deficient.

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Joshua Zelinsky. 2024-02-22. The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number. https://arxiv.org/abs/2402.14234

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