A286520 Number of finite connected sets of pairwise indivisible positive integers greater than one with least common multiple n.

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, 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, 5, 1, 9, 1, 1, 2, 2, 1, 5, 1, 4, 1, 1, 1, 17, 1, 1, 1

Offset: 2

Author

Gus Wiseman, Jul 24 2017

Keywords

• nonn

Comments

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.

Examples

			The a(30)=5 sets are: {30}, {6,10}, {6,15}, {10,15}, {6,10,15}.
		

Crossrefs

Cf. A048143, A054921, A076078, A259936, A281116, A285572, A285573, A286518.

Programs

Mathematica

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]]]]]]]]];
Table[Length[Select[Subsets[Rest[Divisors[n]]],And[!MemberQ[Tuples[#,2],{x_,y_}/;And[x