# Divisor Generating Function?

It is known that $\large \displaystyle \sum _{n=1}^{\infty }\dfrac{\sigma_3(n)}{n^2}e^{-2\pi n}=\dfrac{G}{a} - \dfrac{b\pi^c}{d}$

where $$G$$ is denotes the Catalan's constant

$\displaystyle G=\sum _{n=0}^{ \infty }\frac{\left(-1\right)^n}{\left(2n+1\right)^2},$

$$\sigma_3(n)$$ is defined to be the divisor function

$\displaystyle σ_3(n)=\sum_{d\mid n}d^3,$

And $$a,b,c$$ and $$d$$ are positive integers, with $$b,d$$ coprime. Find $$a+b+c+d$$.

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