editing

approved

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}]

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}]

proposed

editing

editing

proposed

nonn,changed,hard,more

phicuaterA227499[n_]:=Length@Select[cuaternios[n], GCD[Det[#], n]== 1 &];

expo[M_, n_]:= Min@Select[Divisors@phicuaterA227499[n], Mod[MatrixPower[M, #], n]==IdentityMatrix[4]&]; A227477a[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}]

[n_]:= lcm@Table[expo[cuater[n][[i]], n], {i, phicuater[n]}]; lcm[lis_] :={aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; Table[A227477

[n], {n, 2, 10}]

expo[M_, n_]:= Min@Select[Divisors@phicuater[n], Mod[MatrixPower[M, #], n]==IdentityMatrix[4]&]; A227477

expo[M_, n_]:= Min@Select[Divisors@phicuater[n], Mod[MatrixPower[M, #], n]==IdentityMatrix[4]&]; exp[n_]:= lcm@Table[expo[cuater[n][[i]], n], {i, phicuater[n]}]; lcm[lis_] :={aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; Table[exp[n], {n, 2, 10}]A227477

[n], {n, 2, 10}]

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

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

Cf. A227499, A002322.

cuaternios[n_]:=Flatten[Table[{{a, -b, d , -c}, {b, a, -c, -d}, {-d, c, a, -b}, {c, d, ç, ç, b, a}}, {a, n}, {b, n}, {c, n}, {d, n}], 3];

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

cuaternios[n_] := Flatten[Table[{{a, -b, d , -c}, {b, a, -c, -d}, {-d , , c, a, -b}, {c, d, ç, ç, b, a}}, {a, n}, {b, n}, {c, n}, {d, n}], 3];

phicuater[n_] := Length@Select[cuaternios[n], GCD[Det[#], n] == 1 &];

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

exp[n_] := lcm@Table[expo[cuater[n][[i]], n], {i, phicuater[n]}]

lcm[lis_] := lcm[lis] = {aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; Table[exp[n], {n, 2, 10}]