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) $.
Citation: Zhengjin Bu, Zhefeng Xu. Asymptotic formulas for generalized gcd-sum and lcm-sum functions over $ r $-regular integers $ (\bmod\ n^{r}) $[J]. AIMS Mathematics, 2021, 6(12): 13157-13169. doi: 10.3934/math.2021760
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) $.
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Zhengjin Bu, Zhefeng Xu. Asymptotic formulas for generalized gcd-sum and lcm-sum functions over $ r $-regular integers $ (\bmod\ n^{r}) $[J]. AIMS Mathematics, 2021, 6(12): 13157-13169. doi: 10.3934/math.2021760
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