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

Offset: 0

Author

Benoit Jubin, May 12 2008, May 16 2008

Keywords

• nonn

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).

Crossrefs

Cf. A140185, A140186, A140188.

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)