\[\large \sum_{n=2}^\infty \dfrac{\ln (\varsigma(n))}{n^2}\]

Let \(\varsigma(n)\) be the greatest squarefree divisor of \(n\). For example, \( \varsigma(8) = 2, \varsigma(10) = 10, \varsigma(12) = 6\). Evaluate the summation above.

Give your answer to 3 decimal places.

You may use a calculator such as WolframAlpha for the final calculation.

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