# One for All; All for One

Algebra Level 4

Let $$g$$ be a function defined over all positive integers such that $$g(1) = 1$$ and $$\displaystyle\sum_{k=1}^{n} g(k) = n^{2}g(n)$$ for $$n \ge 2.$$

If $$2015 \cdot g(2015) = \dfrac{a}{b},$$ where $$a$$ and $$b$$ are positive coprime integers, then find $$a + b.$$

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