%I A140187
%S A140187 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,
%T A140187 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,
%U A140187 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 A140187 Number of connected groupoids (categories all of whose morphisms are 
               invertible) with n times as many morphisms as objects.
%C A140187 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 A140187 a(n) = sum(A000001(n/k),k|n). (see formula for A140185)
%F A140187 a(n) = 1 + sum(A000001(n/k),k|n). (the 1 accounts for the empty groupoid; 
               see formula for A140185)
%Y A140187 Cf. A140185, A140186, A140188.
%Y A140187 Sequence in context: A119912 A076368 A071049 this_sequence A111607 A117531 
               A105555
%Y A140187 Adjacent sequences: A140184 A140185 A140186 this_sequence A140188 A140189 
               A140190
%K A140187 nonn
%O A140187 0,2
%A A140187 Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008, May 16 2008