AMC 10 2021-fall-b Problem 22

For each integer $n\geq 2$, let $S_n$ be the sum of all products $jk$, where $j$ and $k$ are integers and $1\leq j<k\leq n$. What is the sum of the 10 least values of $n$ such that $S_n$ is divisible by $3$? $\textbf{(A)}\ 196 \textbf{(B)}\ 197 \textbf{(C)}\ 198 \textbf{(D)}\ 199 \textbf{(E)}\ 200$