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

On some functions involving the lcm and gcd of integer tuples