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Order of universal Chevalley group A_7 (q), q = prime power.
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%I #16 Jun 14 2024 22:31:08

%S 5348063769211699200,961721214905722855895197286400,

%T 78099458182389588115529148326215680000,

%U 103044374585338670859375000000000000000000000,170115000551935077294273059250893063598899496222720000,770654129255561941216424578913668563609374922170066534400

%N Order of universal Chevalley group A_7 (q), q = prime power.

%D 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.

%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

%F a(n) = A(A000961(n+1),7) where A(q,n) is defined in A003787. - _Sean A. Irvine_, Sep 18 2015

%t f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 7] & /@ Select[Range[2, 8], PrimePowerQ] (* _Michael De Vlieger_, Sep 18 2015 *)

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E a(5)-a(6) from _Sean A. Irvine_, Sep 18 2015