A003806 Order of universal Chevalley group A_8 (q), q = prime power.

699612310033197642547200, 124190524600592082795473760093457612800, 1341733356588640095264385107865053233298800640000, 78616578542037111790447631835937500000000000000000000000, 39573939034651534226739680064959446854442420750012276098670264320000

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[#, 8] & /@ Select[Range[2, 7], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)

Formula

a(n) = A(A000961(n+1),8) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

Extensions

a(5) from Sean A. Irvine, Sep 18 2015