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arXiv · 2610.10572

The Integer Values of $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$

Jean-Marie De Koninck·Patrick Letendre
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Abstract

We study the set of integers $n \le x$ for which $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$ takes an integer value. We show that the number of such integers is $\ll x^{2/3+ε}$ for all fixed $ε> 0$.

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Jean-Marie De Koninck, Patrick Letendre. 2026-10-04. The Integer Values of $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$. https://arxiv.org/abs/2610.10572

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