A324837 Number of minimal subsets of {1...n} 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, 8, 1, 1, 2, 2, 2, 5, 1, 2, 2, 4, 1, 8, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 16, 1, 2, 3, 1, 2, 8, 1, 3, 2, 8, 1, 7, 1, 2, 3, 3, 2, 8, 1, 5, 1, 2, 1, 16, 2, 2

Offset

1,6

Comments

Note that the elements must be pairwise indivisible divisors of n.

Differs from A303838 at positions {1, 180, 210, ...}. For example, a(210) = 49, A303838(210) = 55. - Gus Wiseman, Apr 01 2019

Links

Gus Wiseman, Table of n, a(n) for n = 1..300

Example

The a(30) = 8 subsets are: {30}, {2,15}, {3,10}, {5,6}, {6,10}, {6,15}, {10,15}, {2,3,5}.

Mathematica

minim[s_]:=Complement[s, First/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];
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[minim[Select[Rest[stableSets[Divisors[n], Divisible]], LCM@@#==n&]]], {n, 100}]

Crossrefs

Cf. A000005, A006126, A074971, A076078, A085945, A285572, A285573, A286518, A286520, A303837, A303838, A324837.

Sequence in context: A168324 A355939 A303838 * A285572 A179926 A066882

Adjacent sequences: A324834 A324835 A324836 * A324838 A324839 A324840

Keyword

nonn

Author

Gus Wiseman, Mar 19 2019

Status

approved