A140186 Number of connected groupoids (categories all of whose morphisms are invertible) with n more morphisms than objects.

2, 1, 2, 2, 1, 2, 3, 5, 2, 2, 2, 5, 2, 2, 3, 15, 1, 5, 2, 5, 3, 2, 3, 15, 3, 2, 6, 4, 2, 4, 7, 51, 1, 4, 3, 14, 1, 2, 4, 14, 1, 6, 4, 4, 3, 3, 6, 52, 2, 5, 2, 7, 1, 15, 4, 13, 3, 2, 2, 13, 4, 2, 18, 267, 1, 4, 3, 5, 1, 9, 7, 50, 2, 2, 4, 4, 2, 6, 8, 52, 15, 2, 3, 15, 1, 2, 3, 14, 1, 10, 3, 5, 4

Offset: 0

Author

Benoit Jubin, May 12 2008

Keywords

• nonn

Comments

a(n) >= A000001(n+1) (number of groups of order n+1).

Crossrefs

Cf. A140185, A140187, A140188.

Formula

a(0) = 2 and if n>0, a(n) = sum(A000001((n+k)/(k^2)),k^2|n+k). (see formula for A140185)