A090751 Number of indecomposable groups of order n.

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, 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, 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

Offset

1,8

Comments

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)).

References

Derek J. S. Robinson, A course in the theory of groups, Graduate texts in mathematics 80, Springer-Verlag, 1982.

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..2047

Crossrefs

Cf. A000001.

Sequence in context: A327372 A374985 A328323 * A344759 A337820 A322127

Adjacent sequences: A090748 A090749 A090750 * A090752 A090753 A090754

Keyword

nonn,nice

Author

Paul Boddington, Feb 03 2004

Extensions

More terms from Christian G. Bower, May 12 2005

Status

approved