On the Difference S(Z(n)) - Z(S(n)

In this paper, we prove that there exist infmitely many positive integers n satisfying S(Z(n))> Z(S(n)) or S(Z(n)) < Z(S(n))

The function equation S(n) = Z(n) 1

For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the pseudo Smarandache function respectively. In this paper we prove that the equation S(n) = Z(n) has infinitely many positive integer solutions n