id:A140187 - OEIS Search Results

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Number of connected groupoids (categories all of whose morphisms are invertible) with n times as many morphisms as objects.

+0
3

1, 2, 3, 3, 5, 3, 6, 3, 10, 5, 6, 3, 13, 3, 6, 5, 24, 3, 13, 3, 13, 6, 6, 3, 33, 5, 6, 10, 12, 3, 14, 3, 75, 5, 6, 5, 34, 3, 6, 6, 32, 3, 17, 3, 12, 9, 6, 3, 99, 5, 13, 5, 13, 3, 33, 6, 30, 6, 6, 3, 39, 3, 6, 12, 342, 5, 14, 3, 13, 5, 14, 3, 104, 3, 6, 10, 12, 5, 17, 3, 98, 25, 6, 3, 43, 5, 6, 5, 29 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`If n>1, a(n) >= 2 + A000001(n) (number of groups of order n), with equality if and only if n is prime (sequence A000040).`
	FORMULA	`a(n) = sum(A000001(n/k),k\|n). (see formula for A140185)` `a(n) = 1 + sum(A000001(n/k),k\|n). (the 1 accounts for the empty groupoid; see formula for A140185)`
	CROSSREFS	`Cf. A140185, A140186, A140188.` `Sequence in context: A119912 A076368 A071049 this_sequence A111607 A117531 A105555` `Adjacent sequences: A140184 A140185 A140186 this_sequence A140188 A140189 A140190`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008, May 16 2008`

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Last modified December 7 08:40 EST 2009. Contains 170430 sequences.

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