# Calculus + Number Theory = Calcumber Theory

Number Theory Level 4

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

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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