JBMO-SL 2021 N6

Given a positive integer $n \ge 2$ , we define $f(n)$ to be the sum of all remainders obtained by dividing $n$ by all positive integers less than $n$ . For example dividing $5$ with $1, 2, 3$ and $4$ we have remainders equal to $0, 1, 2$ and $1$ respectively. Therefore $f(5) = 0 + 1 + 2 + 1 = 4$ . Find all positive integers $n \ge 3$ such that $f(n) = f(n - 1) + (n - 2)$ .