

A286518


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


38



1, 1, 2, 1, 4, 1, 4, 2, 4, 1, 20, 1, 4, 4, 8, 1, 20, 1, 20, 4, 4, 1, 88, 2, 4, 4, 20, 1, 96, 1, 16, 4, 4, 4, 196, 1, 4, 4, 88, 1, 96, 1, 20, 20, 4, 1, 368, 2, 20, 4, 20, 1, 88, 4, 88, 4, 4, 1, 1824, 1, 4, 20, 32, 4, 96, 1, 20, 4, 96, 1, 1688, 1, 4, 20, 20
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OFFSET

2,3


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 4cycle. A set S is said to be connected if G(S) is a connected graph.


LINKS

Table of n, a(n) for n=2..76.


EXAMPLE

The a(6)=4 sets are: {6}, {2,6}, {3,6}, {2,3,6}.


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]]], zsm[#]==={n}&]], {n, 2, 20}]


CROSSREFS

Cf. A048143, A054921, A076078, A259936, A281116, A285572, A285573, A286520.
Sequence in context: A168177 A216864 A263432 * A029205 A229340 A322968
Adjacent sequences: A286515 A286516 A286517 * A286519 A286520 A286521


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jul 24 2017


STATUS

approved



