A325859 Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different product.

1, 1, 1, 1, 1, 1, 4, 4, 11, 11, 28, 28, 60, 60, 140, 241, 299, 299, 572, 572, 971

Offset

0,7

Links

Table of n, a(n) for n=0..20.

Example

The a(1) = 1 through a(9) = 11 subsets:
  {1}  {12}  {123}  {1234}  {12345}  {2356}   {23567}   {123457}  {235678}
                                     {12345}  {123457}  {123578}  {1234579}
                                     {12456}  {124567}  {124567}  {1235789}
                                     {13456}  {134567}  {125678}  {1245679}
                                                        {134567}  {1256789}
                                                        {134578}  {1345679}
                                                        {135678}  {1345789}
                                                        {145678}  {1356789}
                                                        {234578}  {1456789}
                                                        {235678}  {2345789}
                                                        {245678}  {2456789}

Mathematica

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Times@@@Subsets[#, {2}]&]]], {n, 0, 15}]

Crossrefs

The subset case is A196724.

The maximal case is A325859.

The integer partition case is A325856.

The strict integer partition case is A325855.

Heinz numbers of the counterexamples are given by A325993.

Cf. A002033, A108917, A143823, A275972, A325858, A325860, A325861, A325869, A325878, A325879, A325880.

Sequence in context: A168373 A266438 A128499 * A265206 A327684 A231064

Adjacent sequences: A325856 A325857 A325858 * A325860 A325861 A325862

Keyword

nonn,more

Author

Gus Wiseman, May 31 2019

Status

approved