How to check if $phi(n)$ is a perfect square?

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 $n = 34$, $phi(34)=16=4times 4$.

Can we check this without calculating $phi(n)$?