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
Examples
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.
Links
- 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
Programs
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GAP
A296166 := Filtered([1..2015], n -> NumberSmallGroups(n) > Sigma(n));
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Maple
with(GroupTheory): with(numtheory): for n from 1 to 2047 do if NumGroups(n) > sigma(n) then print(n); fi; od;
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Mathematica
Select[Range[10^4], FiniteGroupCount[#] > DivisorSigma[1, #] &] (* Amiram Eldar, Feb 19 2019 *)
Comments