A341548 Number of commutative rings with additive group (Z/nZ)^2.

1, 6, 6, 28, 6, 36, 6, 79, 35, 36, 6, 168, 6, 36, 36

Offset: 1

Author

José María Grau Ribas, Feb 14 2021

Keywords

• nonn
• mult
• more

Comments

It appears that a(16)=230, but it is preferable to wait for someone to confirm it.

Links

• B. Fine, Classification of Finite Rings of Order p^2, Mathematics Magazine, 66(4) (1993), 248-252.
• C. R. Fletcher, Rings of Small Order, The Mathematical Gazette, 64(427) (1980), 9-22.
• Christof Nöbauer, Numbers of rings on groups of prime power order
• Christof Nöbauer, Home page

Crossrefs

Cf. A341547, A341201, A341202, A037234, A037291, A127708, A127707, A037289, A037290, A038036, A307000, A339948, A000005.

Programs

Mathematica

Clear[phi]; phi[p_, 1] := 6;  phi[2,2] = 28; phi[2,3] = 79;  phi[3,2] = 35; phi[n_]:= Module[{aux = FactorInteger[n]}, Product[phi[aux[[i, 1]], aux[[i, 2]]], {i, Length[aux]}]];