A325861 Number of maximal subsets of {1..n} such that every pair of distinct elements has a different quotient.

1, 1, 1, 1, 3, 3, 6, 6, 9, 13, 32, 32, 57, 57, 140, 229, 373, 373, 549, 549, 825

Offset: 0

Author

Gus Wiseman, May 31 2019

Keywords

• nonn
• more

Examples

			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}
		

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.

Cf. A002033, A103300, A143823, A196724, A325859, A325868, A325869.

Programs

Mathematica

fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],UnsameQ@@Divide@@@Subsets[#,{2}]&]]],{n,0,10}]