Dirichlet series of GCD

\[\large \sum_{n=1}^\infty \dfrac{\gcd(n,2016)}{n^2}= \dfrac{a}{b}\pi^2\]

If the equation above holds true for positive integers \(a\) and \(b\), find \(a+b\).

Clarification:
\(\gcd(m,n) \) denotes the greatest common divisor of \(m\) and \(n\).

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