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%I #33 Apr 15 2016 13:54:27
%S 491,668,844,1183,1474,1961,2293,2936,4190,4686,6244,7363,7999,9266,
%T 11456,13835,14766,17449,19348,20419,23578,25781,29375,34549,37228,
%U 38644,41471,43018,46001,57454,60913,66371,68263,77960,80016,86254,92689,97076,103946,111005,113496
%N Erroneous version of A271811 (but for odd primes only).
%C Previous name was "Number of non-abelian groups of order prime(n)^6".
%H Rodney James, <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0559207-0">The groups of order p^6 (p an odd prime)</a>, Math. Comp. 34 (1980), 613-637.
%H M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee, <a href="http://dx.doi.org/10.1016/j.jalgebra.2003.11.012">Groups and nilpotent Lie rings whose order is the sixth power of a prime</a>, J. Algebra, 278 (2004), 383-401.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = (13*p^2 + 145*p + 1338 + 80*gcd(p-1,3) + 45*gcd(p-1,4) + 8*gcd(p-1, 5) + 8*gcd(p-1,6))/4 for n>2 and where p = prime(n). See [Rodney James].
%o (PARI) a(n) = if (n==2, 491, my(p=prime(n)); (13*p^2 + 145*p + 1338 + 80*gcd(p-1, 3) + 45*gcd(p-1, 4) + 8*gcd(p-1, 5) + 8*gcd(p-1, 6))/4);
%Y Cf. A000001 (groups), A060689 (non-abelian groups),
%Y Cf. A232106, A271664.
%Y Cf. A030516 (primes^6)
%Y Cf. A271811.
%K nonn
%O 2,1
%A _Michel Marcus_, Apr 12 2016