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

Author

Paul Boddington, Feb 03 2004

Keywords

• nonn
• nice

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.

Extensions

More terms from Christian G. Bower, May 12 2005