# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a227477 Showing 1-1 of 1 %I A227477 #18 Jul 19 2013 14:17:38 %S A227477 1,2,24,4,120,24,336,8,72,120 %N A227477 Exponent of the group of Lipschitz quaternions in a reduced system modulo n. %t A227477 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}] %Y A227477 Cf. A227499, A002322. %K A227477 nonn,hard,more %O A227477 1,2 %A A227477 _José María Grau Ribas_, Jul 13 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE