Let $\phi$ be a Euler function. (i.e. $\phi(n)=$ the number of the set $\{m \in \mathbb{N} | (n,m)=1 \text{ and } 1\le m \le n \}$
When $(n,m)=1$, it is known $\phi(nm)=\phi(n)\phi(m)$.
I am wondering whether the converse is ture. I mean, if $\phi(nm)=\phi(n)\phi(m)$, then $m,n$ should be coprime? If not, is there any counterexample?
Thank you very much!
