Dirichlet series of GCD

n=1gcd(n,2016)n2=abπ2\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 aa and bb, find a+ba+b.

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

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