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We give an algorithm to enumerate all primitive abundant numbers (briefly,PANs) with a fixed $\Omega$ (the number of prime factors counted with theirmultiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANsand square-free PANs up to $\Omega=7$ and count all odd PANs and oddsquare-free PANs up to $\Omega=8$. We find primitive weird numbers (briefly,PWNs) with up to 16 prime factors, improving the previous results of[Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have beengiven. The largest PWN we find has 14712 digits: as far as we know, this is thelargest example existing, the previous one being 5328 digits long [Melfi]. Wefind hundreds of PWNs with exactly one square odd prime factor: as far as weknow, only five were known before. We find all PWNs with at least one odd primefactor with multiplicity greater than one and $\Omega = 7$ and prove that thereare none with $\Omega < 7$. Regarding PWNs with a cubic (or higher) odd primefactor, we prove that there are none with $\Omega\le 7$, and we did not findany with larger $\Omega$. Finally, we find several PWNs with 2 square odd primefactors, and one with 3 square odd prime factors. These are the first suchexamples.

Primitive abundant and weird numbers with many prime factors