The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912223713034240 |
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| author | Zelinsky, Joshua |
| author_facet | Zelinsky, Joshua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number Zelinsky, Joshua Number Theory 11A25, 11N64 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. |
| title | The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number |
| topic | Number Theory 11A25, 11N64 |
| url | https://arxiv.org/abs/2402.14234 |