When do $\varphi(n)=n-1$, $\varphi(2n)=2\varphi(n)$ and $\varphi(n^k)=n^{k-1}\varphi(n)$ hold?

Initializing...

When do $\varphi(n)=n-1$, $\varphi(2n)=2\varphi(n)$ and $\varphi(n^k)=n^{k-1}\varphi(n)$ hold? · Prove2Me