cp's OEIS Frontend

A296166 Numbers n such that the number of groups of order n exceeds the sum of divisors of n.

%I A296166 #22 Feb 19 2019 10:05:55
%S A296166 64,128,192,256,288,320,384,448,512,576,640,768,864,896,960,1024,1152,
%T A296166 1280,1344,1408,1440,1536,1600,1664,1728,1792,1920,2048,2112,2176,2187
%N A296166 Numbers n such that the number of groups of order n exceeds the sum of divisors of n.
%C A296166 It seems that 1 is the only number such that the number of groups equals the sum of the divisors and that for almost all numbers the sum of the divisors exceeds the number of groups.
%H A296166 H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://dx.doi.org/10.1142/S0218196702001115">A Millennium Project: Constructing Small Groups</a>, Internat. J. Algebra and Computation, 12 (2002), 623-644.
%H A296166 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>, June 2000.
%H A296166 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A296166 Sequence is { n | A000001(n) > A000203(n) }.
%e A296166 64 is in the sequence because 267 = A000001(64) > A000203(64) = 127.
%e A296166 128 is in the sequence because 2328 = A000001(128) > A000203(128) = 255.
%e A296166 1920 is in the sequence because 241004 = A000001(1920) > A000203(1920) = 6120.
%p A296166 with(GroupTheory): with(numtheory):
%p A296166 for n from 1 to 2047 do if NumGroups(n) > sigma(n) then print(n); fi; od;
%t A296166 Select[Range[10^4], FiniteGroupCount[#] > DivisorSigma[1, #] &] (* _Amiram Eldar_, Feb 19 2019 *)
%o A296166 (GAP) A296166 := Filtered([1..2015], n -> NumberSmallGroups(n) > Sigma(n));
%Y A296166 Subsequence of A090052.
%Y A296166 Cf. A000001, A000203.
%K A296166 nonn,more
%O A296166 1,1
%A A296166 _Muniru A Asiru_, Dec 06 2017