This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140185 #9 Jul 28 2020 11:31:42 %S A140185 1,1,1,1,3,1,2,1,6,3,2,1,6,1,2,1,17,1,6,1,6,2,2,1,17,3,2,6,5,1,4,1,57, %T A140185 1,2,1,19,1,2,2,16,1,6,1,5,3,2,1,58,3,6,1,6,1,17,2,15,2,2,1,14,1,2,5, %U A140185 284,1,4,1,6,1,4,1,61,1,2,4,5,1,6,1,58,18,2,1,17,1,2,1,14,1,12,1,5,2 %N A140185 Number of connected groupoids (categories all of whose morphisms are invertible) with n morphisms. %C A140185 a(n) >= A000001(n) (number of groups of order n), with equality if and only if n is squarefree (sequence A005117). %F A140185 a(0) = 1 and if n>0, a(n) = sum(A000001(n/(k^2)),k^2|n). Indeed, if b(n,k) is the number of connected groupoids with n morphisms and k objects, then the only nonzero values are b(0,0) = 1 and b(m.k^2,k) = A000001(m) with m,k>0. %Y A140185 Cf. A140186, A140187, A140188, A140189. %K A140185 nonn %O A140185 0,5 %A A140185 _Benoit Jubin_, May 12 2008