2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132029In this paper we extend the Smarandache function from the set $N*$ of positive integers to the set $Q$ pf rational numbers. Using the inverse formula, this function is also regarded as a generating function. We put in evidence a procedure to construct a (numerical) function starting from a given function in two particular cases. Also, connections between this function and Euler totient function as well as with Riemann zeta function are established.15 pages, one figureGeneral Mathematics11A25text