Math Help - Phi Function Proof

1. Phi Function Proof

Show that there are infinitely many integers n for which $\phi(n)$ is a perfect square. Hint: Consider $n = 2^{2k + 1}$

I'm trying a proof by induction but I get stuck when considering the k + 1th term.
When p is prime, $\phi(p^a)=p^a(1-\frac{1}{p})$. Therefore, $\phi(2^{2k+1})=p^{2k+1}(1-\frac{1}{2})=p^{2k}=(p^k)^2$