A285572 Number of finite sets of pairwise indivisible positive integers with least common multiple n.

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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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}]

Crossrefs

Cf. A000666, A006126, A048143, A054921, A076078, A076413, A285573.

Sequence in context: A355939 A303838 A324837 * A179926 A066882 A300831

Adjacent sequences: A285569 A285570 A285571 * A285573 A285574 A285575

Keyword

nonn

Author

Gus Wiseman, Apr 21 2017

Status

approved