HMMT November 2024 T10

For each positive integer $n$, let $f(n)$ be either the unique integer $r \in\{0,1, \ldots, n-1\}$ such that $n$ divides $15 r-1$, or 0 if such $r$ does not exist. Compute

$$f(16)+f(17)+f(18)+\cdots+f(300) .$$