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arXiv · 2501.04209

Kullback-Leibler divergence and primitive non-deficient numbers

Joshua Zelinsky·Kyle Zhang
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Abstract

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 $n$.

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Joshua Zelinsky, Kyle Zhang. 2025-01-08. Kullback-Leibler divergence and primitive non-deficient numbers. https://arxiv.org/abs/2501.04209

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