This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Clear[phi]; phi[1] = 1; phi[p_,1] := 8; phi[2,2] = 66;
phi[2,3] = 301; phi[3,2] = 175; phi[n_]:= Module[{aux = FactorInteger[n]}, Product[phi[aux[[i, 1]], aux[[i, 2]]], {i, Length[aux]}]];
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]}]];
For n=2:
Z/2Z<x,y>/(x^2, y^2, y*x),
Z/2Z<x,y>/(x^2, y^2, y*x + x*y),
Z/2Z<x,y>/(x^2, y^2, y*x + 1 + x*y),
so a(2)=3.
For n=3, a complete family of non-isomorphic cases {A,B,a,b,c,d} are:
{0,0,0,0,0,0}, {0,0,0,0,0,1}, {0,0,0,0,0,2}, {0,0,1,0,0,2},
{0,1,0,0,0,1}, {0,1,0,0,0,2}, {0,1,0,1,0,0}, {0,2,0,0,0,1}, {0,2,0,0,0,2},
{1,0,0,0,1,0}, {1,1,0,0,0,1}, {1,1,1,1,2,0}, {1,2,0,0,0,1},
so a(3)=13.
a[1]=1; a[p_,1]:= (12 + (p - 1)/2); a[2, 1]=3; a[2,2]= 97; a[2,3]=624; a[3, 2]=67; a[n_]:=Module[{aux=FactorInteger[n]},Product[a[aux[[i,1]], aux[[i,2]]], {i, Length[aux]}]]; Table[a[n], {n, 1, 15}]
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