Kullback-Leibler divergence and primitive non-deficient numbers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929699961176064 |
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| author | Zelinsky, Joshua Zhang, Kyle |
| author_facet | Zelinsky, Joshua Zhang, Kyle |
| contents | Let $H(n) = \prod_{p|n}\frac{p}{p-1}$ where $p$ ranges over the primes which divide $n$. It is well known that if $n$ is a primitive non-deficient number, then $H(n) > 2$. We examine inequalities of the form $H(n)> 2 + f(n)$ for various functions $f(n)$ where $n$ is assumed to be primitive non-deficient and connect these inequalities to applying the Kullback-Leibler divergence to different probability distributions on the set of divisors of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kullback-Leibler divergence and primitive non-deficient numbers Zelinsky, Joshua Zhang, Kyle Number Theory 11A25 Let $H(n) = \prod_{p|n}\frac{p}{p-1}$ where $p$ ranges over the primes which divide $n$. It is well known that if $n$ is a primitive non-deficient number, then $H(n) > 2$. We examine inequalities of the form $H(n)> 2 + f(n)$ for various functions $f(n)$ where $n$ is assumed to be primitive non-deficient and connect these inequalities to applying the Kullback-Leibler divergence to different probability distributions on the set of divisors of $n$. |
| title | Kullback-Leibler divergence and primitive non-deficient numbers |
| topic | Number Theory 11A25 |
| url | https://arxiv.org/abs/2501.04209 |