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In a paper in the American Mathematical Monthly, the corresponding authorasks for an asymptotic of a gcd-sum function  \begin{align}\sum_{ab\leq N}\tau(\gcd(a,b))\label{eqn:taugcdsum}\end{align}We extensively study generalizations of the sum in the aforementioned paper andestablish asymptotic results using elementary methods only.

Asymptotic Result of A Generalization of A GCD-Sum