D-Power Permutations

Let N be a positive integer and S = {1, 2, 3, ..., N}. For a given positive integer d the function f : S --> S is called d-power permutation if there exists a bijection g : S --> S such that g ( g ( ... g ( x ) ... ) ) = f(x) for each x from S , where g is repeated exactly d times. You are given some bijection f : S --> S and a positive integer D. You need to find the number of those d such that