The function $f$ is defined on positive integers : if $n$ has prime factorization $p^{k_1}_{1} p^{k_2}_{2} ...p^{k_t}_{t}$ then $f(n) = (p_1-1)^{k_1+1}(p_2-1)^{k_2+1}...(p_t-1)^{k_t+1}$. If we keep using this function repeatedly, starting from any positive integer $n$, we will always get to $1$ after some number of steps. What is the smallest integer $n$ for which we need exactly $6$ steps to get to $1$?