# A squarefree function?

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

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.