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The Integer Values of ∑i=1n1/gcd(n,i)
Abstract
We study the set of integers n ≤ x for which ∑i=1n1/gcd(n,i) takes an integer value. We show that the number of such integers is ≪ x2/3+ε for all fixed ε> 0.
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BibTeX
@misc{koninck2026integer,
title = {{The Integer Values of $\sum_i=1^n\frac1\gcd(n,i)$}},
author = {Jean-Marie De Koninck and Patrick Letendre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10572},
eprint = {2610.10572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10572},
}
RIS
TY - UNPB
TI - The Integer Values of ∑_i=1^n1/gcd(n,i)
AU - Jean-Marie De Koninck
AU - Patrick Letendre
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.10572
UR - https://arxiv.org/abs/2610.10572
AB - We study the set of integers n ≤ x for which ∑_i=1^n1/gcd(n,i) takes an integer value. We show that the number of such integers is ≪ x^2/3+ε for all fixed ε> 0.
ER -