An equation involving the F.Smarandache multiplicative function

For any positive integer n, we call an arithmetical function f(n) as the F.Smarandache multiplicative function if f(1) = 1, and if n > 1, n = p1 1 p α2 2 · · · pk k be the fractorization of n into prime powers, then f(n) = max 1≤i≤k {f(pi i )}. For example, the function S(n) = min{m : m ∈ N, n|m!} is a F.Smarandache multiplicative function. From the definition of S(n), it is easy to see that if n = p1 1 p α2 2 · · · pk k be the fractorization of n into prime powers, we have