For each integer $n\geq 2$, let $S_n$ be the sum of all products $jk$, where $j$ and $k$ are integers and $1\leq j<k\leq n$. Find the sum of the $10$ least values of $n$ such that $S_n$ is divisible by $3$.

Let's think step by step and output the final answer within \boxed{}.
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