A003801 Order of universal Chevalley group A_3 (q) (or D_3 (q)), q = prime power.

20160, 12130560, 987033600, 29016000000, 4635182361600, 34558531338240, 203039372390400, 4139330225184000, 50858076935877120, 1148120010326016000, 2851903720876769280, 15136750711925049600

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
• H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Programs

Mathematica

f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 3] & /@ Select[Range[2, 22], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)

Formula

a(n) = A(A000961(n+1),3) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015