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

2,11

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.

Links

Table of n, a(n) for n=2..87.

Example

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

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<y, Divisible[y, x]]], zsm[#]==={n}]&]], {n, 2, 20}]

Crossrefs

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

Sequence in context: A340596 A340654 A303837 * A320105 A120698 A338411

Adjacent sequences: A286517 A286518 A286519 * A286521 A286522 A286523

Keyword

nonn

Author

Gus Wiseman, Jul 24 2017

Status

approved