|
%I #2 Mar 31 2012 10:31:22
%S 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,
%T 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,
%U 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
%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.
%K nonn
%O 0,2
%A _Benoit Jubin_, May 12 2008, May 16 2008
|
