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A229292
Exponent of the group of 2 X 2 invertible matrices over Z/nZ.
1
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
1,2
LINKS
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)).
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved