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 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 (list; graph; refs; listen; history; text; internal format)
 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 4-cycle. A set S is said to be connected if G(S) is a connected graph. LINKS 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

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Last modified September 23 08:18 EDT 2020. Contains 337295 sequences. (Running on oeis4.)