# Oldest problem on Brilliant

$A=\displaystyle \sum _{ n=0 }^{ \infty }{ \frac {(-1)^n \tau(2n+1) }{2n+1 } }$

Given that $$\tau(N)$$ denotes the number of positive integer divisors of $$N$$. Find $$\left\lfloor 100000A \right\rfloor$$.

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