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

Author

Gus Wiseman, Mar 19 2019

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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}]