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
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.
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Muniru A Asiru, Dec 06 2017
STATUS
approved