A calculus problem by <> <>

Calculus Level 3

Let \(\mathbb S\) denote the set of all the positive divisors of 3600. Compute

\[ \sum_{a \in \mathbb S} \int_0^{100} \{ ax \} \, dx . \]

\(\)
Notation: \( \{ \cdot \} \) denotes the fractional part function.

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