On some functions involving the lcm and gcd of integer tuples

Abstract

In this paper an explicit formula for the number of tuples of positive integers having the same lowest common multiple n is derived, and some of the properties of the resulting arithmetic function are analyzed. The tuples having also the same greatest common divisor are investigated, while some novel or existing integer sequences are recovered as particular cases. A formula linking the gcd and lcm for tuples of integers is also presented.