A227477 Exponent of the group of Lipschitz quaternions in a reduced system modulo n.

1, 2, 24, 4, 120, 24, 336, 8, 72, 120

Offset

1,2

Links

Table of n, a(n) for n=1..10.

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]; A227499[n_]:=Length@Select[cuaternios[n], GCD[Det[#], n]== 1 &]; cuater[n_] := Select[cuaternios[n], GCD[Det[#], n] == 1 &]; exp[1]=1; expo[M_, n_]:= Min@Select[Divisors@A227499[n], Mod[MatrixPower[M, #], n] == IdentityMatrix[4]&]; a[n_] := lcm@Table[expo[cuater[n][[i]], n], {i, A227499[n]}]; lcm[lis_] := {aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; Table[a[n], {n, 2, 10}]

Crossrefs

Cf. A227499, A002322.

Sequence in context: A100816 A079612 A329263 * A351850 A066585 A278563

Adjacent sequences: A227474 A227475 A227476 * A227478 A227479 A227480

Keyword

nonn,hard,more

Author

José María Grau Ribas, Jul 13 2013

Status

approved