I understand the totient function, but I am struggling to figure out how to do the process in reverse.
For example, calculating $\phi(n)$ for $n = 240$ is fairly straightforward; I can simply take the prime factorization of the $n$ and use it to solve for the result: $\phi(240) = 64$. However, solving for all $n$ when $\phi(n) = 12$ seems to be much less formulaic. Is there a process for solving "in reverse" this way?