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

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 Bordellès (2007), and extend certain related results of Hilberdink and Tóth (2016). We also formulate some conjectures and open problems.

14 pages, revised

Cited by in corpus (4)

• On certain sums of arithmetic functions involving the gcd and lcm of two positive integers
• Additive arithmetic functions meet the inclusion-exclusion principle: Asymptotic formulas concerning the GCD and LCM of several integers
• Estimates for $k$-dimensional spherical summations of arithmetic functions of the GCD and LCM
• On the reciprocal sum of lcm of k-tuples