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A090751
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Number of indecomposable groups of order n.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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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 prod((1-n^(-s))^(-a(n)),n>=2).
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REFERENCES
| Derek J. S. Robinson, A course in the theory of groups, Graduate texts in mathematics 80, Springer-Verlag, 1982.
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CROSSREFS
| Sequence in context: A141901 A200473 A180172 * A030369 A023520 A082062
Adjacent sequences: A090748 A090749 A090750 * A090752 A090753 A090754
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KEYWORD
| nonn,nice,more
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AUTHOR
| Paul Boddington (psb(AT)maths.warwick.ac.uk), Feb 03 2004
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2005
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