Integrals I: Feynman's Trick · Superchallenge problem

Let $A$ be the set of integers $n$ with $1 \le n \le 2025$ and $\gcd(n, 2025) = 1$. For a nonnegative integer $j$ let $S(j) = \displaystyle\sum_{n\in A} n^j$. How many integers $j$ with $0 \le j \le 24$ make $S(j)$ divisible by $2025$?