login
A325861
Number of maximal subsets of {1..n} such that every pair of distinct elements has a different quotient.
15
1, 1, 1, 1, 3, 3, 6, 6, 9, 13, 32, 32, 57, 57, 140, 229, 373, 373, 549, 549, 825
OFFSET
0,5
EXAMPLE
The a(1) = 1 through a(9) = 13 subsets:
{1} {12} {123} {123} {1235} {1235} {12357} {23457} {24567}
{134} {1345} {1256} {12567} {24567} {123578}
{234} {2345} {2345} {23457} {123578} {134567}
{2356} {23567} {125678} {134578}
{2456} {24567} {134567} {135678}
{13456} {134567} {134578} {145678}
{135678} {145789}
{145678} {234579}
{235678} {235678}
{235789}
{345789}
{356789}
{1256789}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Divide@@@Subsets[#, {2}]&]]], {n, 0, 10}]
CROSSREFS
The subset case is A325860.
The maximal case is A325861.
The integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
Sequence in context: A168237 A290966 A049318 * A376449 A079551 A182843
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved