Summary: We consider a generalization of the lcm-sum function, and we give two kinds of asymptotic formulas for the sum of that function. Our results include a generalization of Bordellès's results and a refinement of the error estimate of Alladi's result. We prove these results by the method similar to those of Bordellès.

11A25, 11N37

arithmetic function, lcm-sum function, least common multiple