Sum of reciprocals of products

Number Theory Level pending

Let 2 integers \(a, b\) be chosen such that

\[\begin{cases} 1 \le a < b \le 2017 \\ a + b >2017 \\ \gcd (a,b) = 1 \end{cases} \]

If \(\displaystyle \sum_{a,b}{\frac{1}{ab}} = \dfrac{m}{n}\), for coprime positive integers \(m,n\). Then give your answer as \(m+n\)

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