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arXiv · 2412.00389

Sums related to Euler's totient function

Artyom Radomskii
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Abstract

We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in \mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$.

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Artyom Radomskii. 2024-11-30. Sums related to Euler's totient function. https://arxiv.org/abs/2412.00389

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