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Let ggg be a function defined over all positive integers such that g(1)=1g(1) = 1g(1)=1 and ∑k=1ng(k)=n2g(n)\displaystyle\sum_{k=1}^{n} g(k) = n^{2}g(n)k=1∑ng(k)=n2g(n) for n≥2.n \ge 2.n≥2.
If 2015⋅g(2015)=ab,2015 \cdot g(2015) = \dfrac{a}{b},2015⋅g(2015)=ba, where aaa and bbb are positive coprime integers, then find a+b.a + b.a+b.
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