# Oldest problem on Brilliant

**Number Theory**Level 5

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

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