Let $q_k$ be the k-$th$ positive natural number that is divisible by a square larger than one. How to prove that
$S_n=\sum^n_{k=1} (-1)^{\Omega(q_k)}\cdot{q_k}$ change sign infinitely many times as $n$ increases?
$\Omega(n)$ is the number of (not necessarily different) prime factors of $n$.
I have made some numerical experiments that indicates this conjecture.
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