|
%I #20 Apr 20 2023 18:23:51
%S 0,1,1,1,1,1,1,3,1,1,1,2,1,1,0,8,1,2,1,2,1,1,1,6,1,1,3,1,1,1,1,34,0,1,
%T 0,4,1,1,1,5,1,2,1,1,0,1,1,23,1,2,0,2,1,6,1,5,1,1,1,3,1,1,1,201,0,1,1,
%U 2,0,1,1,19,1,1,1,1,0,2,1,24,9,1,1,3,0,1,0,4,1,2,0,1,1,1,0,121,1,2,0,6,1
%N Number of indecomposable groups of order n.
%C Indecomposable means nontrivial and not a direct product of two proper subgroups. Any finite group G is a direct product of indecomposable groups and the multiset of isomorphism types of indecomposable factors is an invariant of G. Hence A000001 has Dirichlet generating function Product_{n>=2} (1 - n^(-s))^(-a(n)).
%D Derek J. S. Robinson, A course in the theory of groups, Graduate texts in mathematics 80, Springer-Verlag, 1982.
%H Eric M. Schmidt, <a href="/A090751/b090751.txt">Table of n, a(n) for n = 1..2047</a>
%Y Cf. A000001.
%K nonn,nice
%O 1,8
%A _Paul Boddington_, Feb 03 2004
%E More terms from _Christian G. Bower_, May 12 2005
|
