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A285572
Number of finite sets of pairwise indivisible positive integers with least common multiple n.
76
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 9, 1, 1, 2, 2, 2, 6, 1, 2, 2, 4, 1, 9, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 23, 1, 2, 3, 1, 2, 9, 1, 3, 2, 9, 1, 10, 1, 2, 3, 3, 2, 9, 1, 5, 1, 2, 1, 23, 2, 2, 2, 4, 1, 23, 2, 3, 2, 2, 2, 6, 1, 3, 3, 6
OFFSET
1,6
LINKS
EXAMPLE
The a(72)=10 sets are {72}, {8,9}, {8,18}, {8,36}, {9,24}, {18,24}, {24,36}, {6,8,9}, {8,9,12}, {8,12,18}.
MATHEMATICA
nn=50;
stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];
Table[Length[Select[Rest[stableSets[Divisors[n], Divisible]], LCM@@#===n&]], {n, 1, nn}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 21 2017
STATUS
approved