Calculus + Number Theory = Calcumber Theory

\[\Large \mathcal{S} = \sum_{n=1}^{\infty} \dfrac{\tau (n)}{n^4}\]

Find the value of \(\lfloor 10000 \times \mathcal{S} \rfloor\).

Details and Assumptions :

  • \(\tau (n)\) denotes the number of divisors of \(n\).
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