A140187 - OEIS

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A140187

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

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; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`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: A076368 A071049 A171637 * A111607 A117531 A105555` `Adjacent sequences: A140184 A140185 A140186 * 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 February 13 08:12 EST 2012. Contains 205451 sequences.