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A140185
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Number of connected groupoids (categories all of whose morphisms are invertible) with n morphisms.
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4
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1, 1, 1, 1, 3, 1, 2, 1, 6, 3, 2, 1, 6, 1, 2, 1, 17, 1, 6, 1, 6, 2, 2, 1, 17, 3, 2, 6, 5, 1, 4, 1, 57, 1, 2, 1, 19, 1, 2, 2, 16, 1, 6, 1, 5, 3, 2, 1, 58, 3, 6, 1, 6, 1, 17, 2, 15, 2, 2, 1, 14, 1, 2, 5, 284, 1, 4, 1, 6, 1, 4, 1, 61, 1, 2, 4, 5, 1, 6, 1, 58, 18, 2, 1, 17, 1, 2, 1, 14, 1, 12, 1, 5, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n) >= A000001(n) (number of groups of order n), with equality if and only if n is squarefree (sequence A005117).
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LINKS
| B. Jubin, Sequences contributed to the OEIS.
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FORMULA
| a(0) = 1 and if n>0, a(n) = sum(A000001(n/(k^2)),k^2|n). Indeed, if b(n,k) is the number of connected groupoids with n morphisms and k objects, then the only non-zero values are b(0,0) = 1 and b(m.k^2,k) = A000001(m) with m,k>0.
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CROSSREFS
| Cf. A140186, A140187, A140188, A140189.
Sequence in context: A010123 A039620 A008296 * A106790 A078897 A011086
Adjacent sequences: A140182 A140183 A140184 * A140186 A140187 A140188
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KEYWORD
| nonn
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AUTHOR
| Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008
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