# Zeta gcd

$\large \sum_{\gcd(n,2016)=1} \frac{1}{n^{4}} = \dfrac{a}{b}\pi^{c}$

The equation above holds true for positive integers $$a,b$$ and $$c$$ with $$a,b$$ coprime. Find $$a+b+c$$.

Notation: $$\gcd$$ denotes the greatest common divisor function.

×