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A227867 Number of Lipschitz quaternions X such that X^2 == 1 (mod n). 3
1, 8, 14, 32, 32, 112, 58, 32, 110, 256, 134, 448, 184, 464, 448, 32, 308, 880, 382, 1024, 812, 1072, 554, 448, 752, 1472, 974, 1856, 872, 3584, 994, 32, 1876, 2464, 1856, 3520, 1408, 3056, 2576, 1024, 1724, 6496, 1894, 4288, 3520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A quaternion q = a + bi + cj + dk is congruent to 1 (mod n) iff a == 1 (mod n) and b == c == d == 0 (mod n).

LINKS

Table of n, a(n) for n=1..45.

Wikipedia, Hurwitz quaternion

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]; invo[n_] := invo[n] = Length@Select[cuaternios[n], Mod[#.# - IdentityMatrix[4], n] == 0*# &]; Table[invo[n], {n, 1, 25}]

CROSSREFS

Cf. A227477, A227499, A227628.

Sequence in context: A153340 A144842 A273843 * A254034 A225606 A117132

Adjacent sequences:  A227864 A227865 A227866 * A227868 A227869 A227870

KEYWORD

nonn,mult,more

AUTHOR

José María Grau Ribas, Nov 02 2013

STATUS

approved

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Last modified August 20 06:39 EDT 2019. Contains 326139 sequences. (Running on oeis4.)