  In 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.

General Mathematics