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arXiv · 2106.14953

Powerfree sums of proper divisors

Paul Pollack·Akash Singha Roy
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Abstract

Let $s(n):= \sum_{d\mid n,~d<n} d$ denote the sum of the proper divisors of $n$. It is natural to conjecture that for each integer $k\ge 2$, the equivalence \[ \text{$n$ is $k$th powerfree} \Longleftrightarrow \text{$s(n)$ is $k$th powerfree} \] holds almost always (meaning, on a set of asymptotic density $1$). We prove this for $k\ge 4$.

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Paul Pollack, Akash Singha Roy. 2021-06-28. Powerfree sums of proper divisors. https://arxiv.org/abs/2106.14953

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