Sums of weighted averages of gcd-sum functions

摘要

Let gcd(j,k) be the gnstest common divisor of the integers j and k. In this paper, we give several interesting asymptotic formulas for weighted averages of the gcd-sum function f(gcd(j,k)) and the function Sigma d vertical bar k,d(s)vertical bar j(f * mu)(d) for any positive integers j and k, namely