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arXiv · 2408.01936

On the distribution of $\phi(\sigma(n))$

Saunak Bhattacharjee·Anup B. Dixit
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Abstract

Let $\phi(n)$ be the Euler totient function and $\sigma(n)$ denote the sum of divisors of $n$. In this note, we obtain explicit upper bounds on the number of positive integers $n\leq x$ such that $\phi(\sigma(n)) > cn$ for any $c>0$. This is a refinement of a result of Alaoglu and Erd\H{o}s.

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Saunak Bhattacharjee, Anup B. Dixit. 2024-08-04. On the distribution of $\phi(\sigma(n))$. https://doi.org/10.5281/zenodo.12685741

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