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%I #25 Jul 26 2017 10:20:12
%S 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,2,1,5,1,1,1,1,1,
%T 5,1,1,1,3,1,5,1,2,2,1,1,4,1,2,1,2,1,3,1,3,1,1,1,17,1,1,2,1,1,5,1,2,1,
%U 5,1,9,1,1,2,2,1,5,1,4,1,1,1,17,1,1,1
%N Number of finite connected sets of pairwise indivisible positive integers greater than one with least common multiple n.
%C Given a finite set S of positive integers greater than one, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices that are not relatively prime. For example, G({6,14,15,35}) is a 4-cycle. A set S is said to be connected if G(S) is a connected graph.
%e The a(30)=5 sets are: {30}, {6,10}, {6,15}, {10,15}, {6,10,15}.
%t zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c==={},s,zsm[Union[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
%t Table[Length[Select[Subsets[Rest[Divisors[n]]],And[!MemberQ[Tuples[#,2],{x_,y_}/;And[x<y,Divisible[y,x]]],zsm[#]==={n}]&]],{n,2,20}]
%Y Cf. A048143, A054921, A076078, A259936, A281116, A285572, A285573, A286518.
%K nonn
%O 2,11
%A _Gus Wiseman_, Jul 24 2017
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