Asymptotic formulas for generalized gcd-sum and lcm-sum functions over $ r $-regular integers $ (\bmod\ n^{r}) $

Author:

Bu Zhengjin, ,Xu Zhefeng

Abstract

<abstract><p>In this paper we perform a further investigation for $ r $-gcd-sum function over $ r $-regular integers $ (\bmod\ n^{r}) $, and we derive two kinds of asymptotic formulas by making use of Dirichlet product, Euler product and some techniques. Moreover, we also establish estimates for the generalized $ r $-lcm-sum function over $ r $-regular integers $ (\bmod\ n) $.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference14 articles.

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2. O. Bordells, Mean values of generalized gcd-sum and lcm-sum functions, J. Integer Seq., 10 (2007), 1–13.

3. T. Hilberdink, F. Luca, L. Tóth, On certain sums concerning the gcd's and lcm's of k positive integers, Int. J. Number Theory, 16 (2020), 77–90.

4. V. S. R. Prasad, P. A. Reddy, M. G. Rao, On the partial sums of the dirichlet series of the $r$-gcd-sum function, Int. J. Math. Comput. Appl. Res., 3 (2013), 65–76.

5. M. G. Rao, $r$-regular Integers Modulo $n^{r}$, Turkish J. Comput. Math. Edu., 12 (2021), 1047–1053.

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