[seqfan] Five gold rings

[martin_n_fuller]

Would anyone here like to collaborate in calculating the number of rings 
with 32 elements (A027623) and the number of unital rings with 64 
elements (A037291)?  I have some provisional results which are not 
rigorous enough for OEIS.  In particular, I'm not sure about my 
construction method or isomorphism detection.

My results largely agree with the archived version of C. Noebauer's 
webpage.  Provisional results which are new or different:
Additive group (Z2)^5; 783 rings
Additive group (Z2)^3 x Z8; 9881 rings
Additive group (Z2)^2 x (Z4)^2; 224 rings with one (C. Noebauer table 
had 232)
Additive group (Z2)^4 x Z4; 1210 rings with one

Ongoing calculations: all rings with additive group (Z2)^2 x (Z4)^2, and 
unital rings with additive group (Z2)^6.

Martin Fuller