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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 $a+b$ ?