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

0,2

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).

Links

Table of n, a(n) for n=0..88.

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: A279931 A071049 A171637 * A214127 A111607 A327124

Adjacent sequences: A140184 A140185 A140186 * A140188 A140189 A140190

Keyword

nonn

Author

Benoit Jubin, May 12 2008, May 16 2008

Status

approved