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Algebra Level 5

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

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

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