A003800 Order of universal Chevalley group A_2 (q), q = prime power.

168, 5616, 60480, 372000, 5630688, 16482816, 42456960, 212427600, 810534816, 4277145600, 6950204928, 16934047920, 78156525216, 152334000000, 282027786768, 499631102880, 851974934400, 1098404364288

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[#, 2] & /@ Select[Range[2, 36], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)

Formula

a(n) = A(A000961(n+1),2) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015