login
A324837
Number of minimal subsets of {1...n} with least common multiple n.
8
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
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 19 2019
STATUS
approved