A324837 - OEIS

%I #18 May 17 2019 15:21:48

%S 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,

%T 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,

%U 2,8,1,7,1,2,3,3,2,8,1,5,1,2,1,16,2,2

%N Number of minimal subsets of {1...n} with least common multiple n.

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

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

%H Gus Wiseman, <a href="/A324837/b324837.txt">Table of n, a(n) for n = 1..300</a>

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

%t minim[s_]:=Complement[s,First/@Select[Tuples[s,2],UnsameQ@@#&&SubsetQ@@#&]];

%t 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]]]];

%t Table[Length[minim[Select[Rest[stableSets[Divisors[n],Divisible]],LCM@@#==n&]]],{n,100}]

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

%K nonn

%O 1,6

%A _Gus Wiseman_, Mar 19 2019