In this paper we extended the Smarandache function from the set N* of positive integers to the set Q of rational numbers. Using the inversion 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 the Smarandache function and Euler's totient function as with Riemann's zeta function are established.
Comments: 15 pages
[v1] 6 Mar 2010
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