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

64, 128, 192, 256, 288, 320, 384, 448, 512, 576, 640, 768, 864, 896, 960, 1024, 1152, 1280, 1344, 1408, 1440, 1536, 1600, 1664, 1728, 1792, 1920, 2048, 2112, 2176, 2187

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..31.

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.

Gordon Royle, Numbers of Small Groups, June 2000.

Index entries for sequences related to groups

Formula

Sequence is { n | A000001(n) > A000203(n) }.

Example

64 is in the sequence because 267 = A000001(64) > A000203(64) = 127.
128 is in the sequence because 2328 = A000001(128) > A000203(128) = 255.
1920 is in the sequence because 241004 = A000001(1920) > A000203(1920) = 6120.

Maple

with(GroupTheory): with(numtheory):
for n from 1 to 2047 do if NumGroups(n) > sigma(n) then print(n); fi; od;

Mathematica

Select[Range[10^4], FiniteGroupCount[#] > DivisorSigma[1, #] &] (* Amiram Eldar, Feb 19 2019 *)

Prog

(GAP) A296166 := Filtered([1..2015], n -> NumberSmallGroups(n) > Sigma(n));

Crossrefs

Subsequence of A090052.

Cf. A000001, A000203.

Sequence in context: A324487 A258001 A255996 * A355265 A044187 A152691

Adjacent sequences: A296163 A296164 A296165 * A296167 A296168 A296169

Keyword

nonn,more

Author

Muniru A Asiru, Dec 06 2017

Status

approved