[seqfan] A347521 Number of polyominoes with n cells formed by coordinates that are not coprime

[John Mason]

Hi sequence fans
I have looked at this sequence but I don't know how it works.
Could anyone maybe give an explanation of, e.g., a(4)=1, say by
illustrating why 4 of the 5 tetrominoes are excluded and just 1 is included?
I would contact the author but his wiki page says no email address is
available.
Thanks
john