Function and Triangle are Best Friend

Algebra Level 4

A function is defined as f(1)=2017f(1) = 2017 and f(1)+f(2)++f(n)=n2f(n)f(1) + f(2) + \cdots + f(n) = n^2 f(n) for all n>1n > 1. Find f(2017)f(2017).

If you answer can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers, compute a+ba+b.

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