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
Programs
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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}]