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arXiv · 1805.10877

On certain sums concerning the gcd's and lcm's of $k$ positive integers

Titus Hilberdink·Florian Luca·László Tóth
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Abstract

We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd's and lcm's of $k$ positive integers, where $k\ge 2$ is fixed. We refine and generalize an asymptotic formula of Bordell\`{e}s (2007), and extend certain related results of Hilberdink and T\'oth (2016). We also formulate some conjectures and open problems.

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Titus Hilberdink, Florian Luca, László Tóth. 2018-05-28. On certain sums concerning the gcd's and lcm's of $k$ positive integers. https://doi.org/10.1142/s1793042120500049

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