Let $k \in \mathbb{N}$. Define $$F(k) = |\{g : g \ \mbox{is primitive characters modulo}\ k\}|.$$ I would like to calculate $F$, and fine its potential formula.I think for odd prime $p$, $$F(p) = 1.$$
I think if I can prove that $F$ is multiplicative, then it might be possible to find a formula. However, not sure if $F$ is multiplicative, or even $F$ is, I do not see a way to deduce the fact.