Riemann meets Liouville

$S=\sum_{n=1}^{\infty}\frac{(-1)^{\Omega(n)}}{n^4}$

Let $$\Omega(n)$$ denote the number of prime factors of $$n$$, counted with their multiplicities. For example, $$\Omega(2016)=\Omega(2^5\times 3^2\times 7)=5+2+1=8$$.

Submit $$\dfrac{\pi^4}{S}$$ as your answer.

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