Question 175
Find all functions $f: \mathbb{N} \to \mathbb{N}$ such that for every positive integer $m$ the following is true: if we denote by $d_1, d_2, \dots, d_n$ all the divisors of the number $m$, then
$$
f(d_1) \cdot f(d_2) \cdots f(d_n) = m.
$$
$$
f(d_1) \cdot f(d_2) \cdots f(d_n) = m.
$$