TH-TMO 2022 Problem 10

For each positive integers $u$ and $n$ , say that $u$ is a friend of $n$ if and only if there exists a positive integer $N$ that is a multiple of $n$ and the sum of digits of $N$ (in base 10) is equal to $u$ . Determine all positive integers $n$ that only finitely many positive integers are not a friend of $n$ .