[seqfan] "Simple" rings

[Charles Greathouse]

Surely this sequence is already in the OEIS, but I cannot find it:
Number of rings of order n which cannot be expressed as the direct product
of smaller rings.
What are these rings called?

Any of the various definitions of "ring" are of interest here.

For a bonus, I'd like to loop through these (ideally, such rings with 1) in
GAP or something similar. Is this possible? I know there are problems
enumerating small rings so a library of known examples would be fine.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University