How to check if $\phi(n)$ is a perfect square?
Here, $\phi$ is Euler's totient function. That is,$\phi(n)$ counts the positive integers up to a given integer $n$ that are relatively prime to $n$
for example if $n = 34$, $\phi(34)=16=4\times 4$.
Can we check this without calculating $\phi(n)$?