A227628 Number of Lipschitz quaternions X such that X^2 == X (mod n).

1, 2, 14, 2, 32, 28, 58, 2, 110, 64, 134, 28, 184, 116, 448, 2, 308, 220, 382, 64, 812, 268, 554, 28, 752, 368, 974, 116, 872, 896, 994, 2, 1876, 616, 1856, 220, 1408, 764, 2576, 64, 1724, 1624, 1894, 268, 3520, 1108, 2258, 28, 2746, 1504

Offset

1,2

Links

Table of n, a(n) for n=1..50.

C. J. Miguel and R. Serodio, On the Structure of Quaternion Rings over Zp, International Journal of Algebra, Vol. 5, 2011, no. 27, pp. 1313-1325.

Mathematica

cuaternios[n_] := Flatten[Table[{{ a, -b, d, -c}, {b, a, -c, -d}, {-d, c, a, -b}, {c, d, b, a}}, {a, n}, {b, n}, {c, n}, {d, n}], 3]; cuater[n_] := Length@Select[cuaternios[n], Mod[#.# - #, n] == 0*# &]; Table[cuater[n], {n, 1, 100}]

Crossrefs

Cf. A000118, A227477, A227499.

Sequence in context: A368758 A221234 A133420 * A298800 A138907 A336837

Adjacent sequences: A227625 A227626 A227627 * A227629 A227630 A227631

Keyword

nonn,mult

Author

José María Grau Ribas, Jul 18 2013

Status

approved