Excess prime-factor multiplicity
= Excess prime-factor multiplicity
{title2=$\Omega(n)-\omega(n)$}
The nonnegative <arithmetic function> $\Omega(n)-\omega(n)$ counts the repeated occurrences beyond the first of each <prime factor>. Its <expectation> under uniform sampling from $[N]$ is bounded by $\sum_p1/(p(p-1))\le1$, independently of $N$.