Inspired by this Problem of the Week.

Given \(n\) is a positive integer divisible by 3, and the list below consists of \(n\) sums, how many of the sums are divisible by 3?

\[\begin{array}{l} 1 \\ 1 + 2 \\ 1 + 2 + 3 \\ 1 + 2 + 3 + 4 \\ 1 + 2 + 3 + 4 + 5 \\ 1 + 2 + 3 + 4 + 5 + 6 \\ \vdots \\ 1 + 2 + 3 + \cdots + n \\ \end{array}\]

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