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 A227628 Number of Lipschitz quaternions X such that X^2 == X (mod n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A260120 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

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Last modified December 8 08:02 EST 2023. Contains 367662 sequences. (Running on oeis4.)