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arXiv · 2605.17872

A note on the $q$-adic valuation of $\sigma_k(n)$

Olivier Bordellès
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Abstract

In this note, we obtain an exact formula for the $q$-adic valuation of $\sigma_k(n)$ where $q$ is an odd prime, allowing us to derive an explicit upper bound which is asymptotically better than the previous bound obtained by Zhao when $n$ is large and $k \geqslant q-2$. The key parts are played by the LTE lemma and the use of cyclotomic polynomials.

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Olivier Bordellès. 2026-05-18. A note on the $q$-adic valuation of $\sigma_k(n)$. https://arxiv.org/abs/2605.17872

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