Number of permutations

disregardthat

Given a function [tex]f : K \to K[/tex], where [tex]K = \{1,2,...,n-1\}[/tex], how many permutations [tex]\sigma \in S_n[/tex] exists such that [tex]\sigma^{-1} \circ f \circ \sigma = f[/tex] (assuming f(n) = n)?