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Algebra Level 5

Let f:N+Q+f:\mathbb{N}^+ \to \mathbb{Q}^+ satisfies f(1)=2016f(1) = 2016 and i=1nf(i)=n2f(n)\displaystyle \sum_{i=1}^n f(i) = n^2 f(n) for n>1n>1.

If the value of f(2016)f(2016) can be represented as ab\dfrac {a}{b} where aa and bb are coprime positive integers, what is the value of a+ba+b?

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