 Inverse totient problem

Given a positive integer $m$, find all positive integers $n$ satisfying $\phi (n)=m$. For every prime divisor $p$ of a solution, $p-1$ divides $m$, so the possible primes lie in the finite set $\{d+1:d\mid m,d+1\text{ is prime}\}$. Search can then combine the prime powers whose totient contributions multiply to $m$.