\[\large \sum_{n=1}^\infty \frac{2^{\omega(n)}}{n^2}\]

Let \(\omega(n)\) denote the number of distinct prime divisors of \(n\).

If the series above can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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