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Journal Article

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

MPS-Authors
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Luca,  Florian
Max Planck Institute for Mathematics, Max Planck Society;

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Tóth,  László
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1142/S1793042120500049
(Publisher version)

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1805.10877.pdf
(Preprint), 149KB

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Citation

Hilberdink, T., Luca, F., & Tóth, L. (2020). On certain sums concerning the gcd's and lcm's of k positive integers. International Journal of Number Theory, 16(1), 77-90. doi:10.1142/S1793042120500049.


Cite as: https://hdl.handle.net/21.11116/0000-0005-E4CE-2
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.