# Composition of Euler’s \$phi\$ function

I am trying to show that the $$phi(phi(n))$$ is equal to the number of generators of $$mathbb{Z}_n^*$$ for all $$n$$ such that a generator exists.

Generators only exist for cyclic groups, and so I know that $$n$$ must be equal to $$1,2,4,p^k$$, or $$2p^k$$ where $$p$$ is an odd prime and $$k>0$$.

I also know that the number of elements of order $$n$$ (the number of generators) will be equal to $$phi(n)$$

From here though I am unsure where to go. Any help would be greatly appreciated.