This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A208663 #31 Aug 11 2025 10:41:55
%S A208663 1,6,12,16,24,32,48,64,96,128,256,512,1024,2048
%N A208663 Non-Abelian numbers: n such that A000001(n)/A000688(n) is a new record.
%D A208663 H. A. Bender, A determination of the groups of order p^5, Ann. of Math. (2) 29, pp. 61-72 (1927).
%D A208663 H. U. Besche and B. Eick, Construction of Finite Groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.
%D A208663 H. U. Besche and B. Eick, The Groups of Order at Most 1000 Except 512 and 768, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.
%D A208663 H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.
%D A208663 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 134.
%D A208663 M. Hall, Jr. and J. K. Senior, The Groups of Order 2^n (n <= 6). Macmillan, NY, 1964.
%D A208663 G. A. Miller, Determination of all the groups of order 64, Amer. J. Math., 52 (1930), 617-634.
%D A208663 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section XIII.24, p. 481.
%D A208663 M. F. Newman and E. A. O'Brien, A CAYLEY library for the groups of order dividing 128. Group theory (Singapore, 1987), 437-442, de Gruyter, Berlin-New York, 1989.
%D A208663 E. Rodemich, The groups of order 128. J. Algebra 67 (1980), no. 1, 129-142.
%H A208663 J. H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf">Counting groups: gnus, moas and other exotica</a>.
%H A208663 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FiniteGroup.html">Finite Group</a>
%H A208663 M. Wild, <a href="http://www.jstor.org/stable/30037381">The groups of order sixteen made easy</a>, Amer. Math. Monthly, 112 (No. 1, 2005), 20-31.
%H A208663 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e A208663 For a(n)=12, there are 2 Abelian groups and 3 nonabelian groups, so the ratio A000001(12)/A000688(12)=5/2=2.5, which beats the previous record of 2, so 12 is in the sequence.
%t A208663 s = {1}; a = 1; Do[b = FiniteGroupCount[n]/FiniteAbelianGroupCount[n];
%t A208663 If[b > a, a = b; AppendTo[s, n]], {n, 1, 2047}]; s
%Y A208663 Cf. A000001, A000688, A060689, A051532.
%K A208663 nonn,hard,more
%O A208663 1,2
%A A208663 _Ben Branman_, Feb 29 2012
%E A208663 a(14) from _Eric M. Schmidt_, Aug 02 2012