A229292 Exponent of the group of 2 X 2 invertible matrices over Z/nZ.

1, 6, 24, 30, 120, 24, 336, 126, 240, 120, 1320, 120, 2184, 336, 120, 510, 4896, 240, 6840, 120, 336, 1320, 12144, 504, 3120, 2184, 2184, 1680, 24360, 120, 29760, 2046, 1320, 4896, 1680, 240, 50616, 6840, 2184, 2520, 68880, 336, 79464, 1320, 240, 12144

Offset: 1

Author

José María Grau Ribas, Nov 02 2013

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000252, A227477, A316566.

Programs

Mathematica

ex[p_, s_] := LCM[p(p^(2 s) - 1), p - 1]; ex[1] := 1; ex[n_] := {aux = 1; Do[aux = LCM[aux, ex[fa[n][[i, 1]], fa[n][[i, 2]]]], {i, 1, Length[fa[n]]}]; aux}[[1]];Table[ex[n], {n, 1, 111}]

PARI

a(n)=if(n==1,return(1)); my(f=factor(n)); lcm(vector(#f~,i, f[i,1]*lcm((f[i,1]^(2*f[i,2])-1), f[i,1]-1))) \\ Charles R Greathouse IV, Nov 13 2013

Formula

a(p^s) = lcm(p*(p^(2*s) - 1), p - 1); if gcd(m,n)=1 then a(n*m) = lcm(a(n), a(m)).