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 A140187 Number of connected groupoids (categories all of whose morphisms are invertible) with n times as many morphisms as objects. 2

%I

%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

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