cp's OEIS Frontend

A271811 Number of non-abelian groups of order prime(n)^6.

%I A271811 #25 Nov 26 2017 05:30:58
%S A271811 256,493,673,849,1181,1465,1933,2253,2865,4057,4529,6001,7053,7653,
%T A271811 8841,10897,13125,14001,16509,18281,19285,22233,24285,27637,32461,
%U A271811 34953,36273,38901,40345,43117,53769,56981,62053,63813,72817,74729,80521,86493,90561,96937,103485,105801,117281
%N A271811 Number of non-abelian groups of order prime(n)^6.
%C A271811 A000688(p^6) is 11 for all prime p.
%H A271811 Muniru A Asiru, <a href="/A271811/b271811.txt">Table of n, a(n) for n = 1..1229</a>
%H A271811 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 A271811 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A271811 a(n) = A232106(n) - 11.
%F A271811 a(n) = A060689(prime(n)^6) = A060689(A030516(n)).
%F A271811 For a prime p > 3, the number of non-abelian groups of order p^6 is 3p^2 + 39p + 333 + 24 gcd(p - 1, 3) + 11 gcd(p - 1, 4) + 2 gcd(p - 1, 5).
%t A271811 Table[FiniteGroupCount[#] - FiniteAbelianGroupCount[#] &[Prime[n]^6], {n, 43}] (* _Michael De Vlieger_, Apr 15 2016, after _Vladimir Joseph Stephan Orlovsky_ at A060689 *)
%o A271811 (PARI) a(n) = if (n==1, 256, if (n==2, 493, my(p=prime(n)); 3*p^2 + 39*p + 333 + 24*gcd(p - 1, 3) + 11*gcd(p - 1, 4) + 2*gcd(p - 1, 5)));
%o A271811 (GAP) A271811 := Concatenation([256, 493], List(Filtered([5..10^4], IsPrime), p -> 3 * p^2 + 39 * p + 333 + 24 * Gcd(p-1, 3) + 11 * Gcd(p-1, 4) + 2 * Gcd(p-1,5))); # _Muniru A Asiru_, Nov 18 2017
%Y A271811 Cf. A000688, A030516, A060689, A232106, A271664.
%K A271811 nonn
%O A271811 1,1
%A A271811 _Altug Alkan_, Apr 14 2016