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We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd’s and lcm’s of [Formula: see text] positive integers, where [Formula: see text]… Click to show full abstract
We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd’s and lcm’s of [Formula: see text] positive integers, where [Formula: see text] is fixed. We refine and generalize an asymptotic formula of Bordellès [Mean values of generalized gcd-sum and lcm-sum functions, J. Integer Seq. 10 (2007) Article ID:07.9.2, 13[Formula: see text]pp], and extend certain related results of Hilberdink and Tóth [On the average value of the least common multiple of [Formula: see text] positive integers, J. Number Theory 169 (2016) 327–341]. We also formulate some conjectures and open problems.
Journal Title: International Journal of Number Theory
Year Published: 2019
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