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 $a + b.$