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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

Cf. A000252, A227477, A316566.

Sequence in context: A275302 A201596 A128459 * A147826 A247271 A065743

Adjacent sequences:  A229289 A229290 A229291 * A229293 A229294 A229295

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Nov 02 2013

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)