Proof Writing & Problem Solving · Challenge problem

The proof that $\sqrt2$ is irrational uses the step "if $2 \mid a^2$, then $2 \mid a$". A student adapts it to $\sqrt n$ and needs the step "if $n \mid a^2$, then $n \mid a$" to hold for every integer $a$. For how many integers $n$ with $2 \le n \le 50$ is $\sqrt n$ irrational but this step false?