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%I #9 Jul 28 2020 11:31:42
%S 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 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 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 Number of connected groupoids (categories all of whose morphisms are invertible) with n morphisms.
%C a(n) >= A000001(n) (number of groups of order n), with equality if and only if n is squarefree (sequence A005117).
%F 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 Cf. A140186, A140187, A140188, A140189.
%K nonn
%O 0,5
%A _Benoit Jubin_, May 12 2008
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