A226756 - OEIS

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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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..49.

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}]

PROG

(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

CROSSREFS

Cf. A087726.

Sequence in context: A014002 A301787 A029625 * A029631 A187062 A153340

Adjacent sequences: A226753 A226754 A226755 * A226757 A226758 A226759

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Jun 16 2013

STATUS

approved