Question 110
For a given positive integer $n$, we define $\varphi(n)$ to be the number of positive integers less than or equal to $n$ which share no common prime factors with $n$. Find all positive integers $n$ for which
$$
\varphi(2019 n)=\varphi\left(n^{2}\right)
$$
$$
\varphi(2019 n)=\varphi\left(n^{2}\right)
$$