A226756 Number of elements X in the matrix ring M_2(Z_n) such that X^2 == X (mod n).
1, 8, 14, 26, 32, 112, 58, 98, 110, 256, 134, 364, 184, 464, 448, 386, 308, 880, 382, 832, 812, 1072, 554, 1372, 752, 1472, 974, 1508, 872, 3584, 994, 1538, 1876, 2464, 1856, 2860, 1408, 3056, 2576, 3136, 1724, 6496, 1894, 3484, 3520, 4432, 2258, 5404, 2746
Offset: 1
Crossrefs
Cf. A087726.
Programs
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Mathematica
ring[n_] := Flatten[Table[{{a, b}, {c, d}}, {a, 0, n - 1}, {b, 0, n - 1}, {c, 0, n - 1}, {d, 0, n - 1}], 3]; a[n_] := Length@Select[ring[n], Mod[#.#, n] == # &]; Table[a[n], {n, 44}] -
PARI
a(n) = sum(i=0, n-1, sum(j=0, n-1, sum(k=0, n-1, sum(l=0, n-1, m = Mod([i,j;k,l], n); m^2 == m)))); \\ Michel Marcus, Apr 04 2016