%N Number of connected groupoids (categories all of whose morphisms are invertible) with n times as many morphisms as objects.
%C 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).
%F a(n) = sum(A000001(n/k),k|n). (see formula for A140185)
%F a(n) = 1 + sum(A000001(n/k),k|n). (the 1 accounts for the empty groupoid; see formula for A140185)
%Y Cf. A140185, A140186, A140188.
%A _Benoit Jubin_, May 12 2008, May 16 2008