Inspired by the oldest problem on brilliant

\[A=\sum _{n=1}^{\infty }\frac{\left(-1\right)^nd\left(n\right)}{n^2}\]

Find \(\left\lfloor 10000A \right\rfloor\)

Note: \(d(n)\) denotes the number of positive integer divisors of \(n\).


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