id:A140185 - OEIS Search Results

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Number of connected groupoids (categories all of whose morphisms are invertible) with n morphisms.

+0
5

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; listen)

	OFFSET	`0,5`
	COMMENT	`a(n) >= A000001(n) (number of groups of order n), with equality if and only if n is square-free (sequence A005117).`
	LINKS	`B. Jubin, Sequences contributed to the OEIS.`
	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.`
	CROSSREFS	`Cf. A140186, A140187, A140188, A140189.` `Adjacent sequences: A140182 A140183 A140184 this_sequence A140186 A140187 A140188` `Sequence in context: A010123 A039620 A008296 this_sequence A106790 A078897 A011086`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008`

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Last modified October 6 16:13 EDT 2008. Contains 144667 sequences.

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