A325860 Number of subsets of {1..n} such that every pair of distinct elements has a different quotient.

1, 2, 4, 8, 14, 28, 52, 104, 188, 308, 548, 1096, 1784, 3568, 6168, 10404, 16200, 32400, 49968, 99936, 155584, 256944, 433736, 867472, 1297504, 2026288, 3387216, 5692056, 8682912, 17365824, 25243200, 50486400, 78433056, 125191968, 206649216, 328195632

Offset

0,2

Comments

Also subsets of {1..n} such that every orderless pair of (not necessarily distinct) elements has a different product.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..50

Example

The a(0) = 1 through a(4) = 14 subsets:
  {}  {}   {}    {}     {}
      {1}  {1}   {1}    {1}
           {2}   {2}    {2}
           {12}  {3}    {3}
                 {12}   {4}
                 {13}   {12}
                 {23}   {13}
                 {123}  {14}
                        {23}
                        {24}
                        {34}
                        {123}
                        {134}
                        {234}

Mathematica

Table[Length[Select[Subsets[Range[n]], UnsameQ@@Divide@@@Subsets[#, {2}]&]], {n, 0, 20}]

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, A108917, A143823, A196723, A196723, A196724, A325855, A325858, A325859, A325868, A325869.

Sequence in context: A096590 A068912 A164176 * A217932 A215978 A018086

Adjacent sequences: A325857 A325858 A325859 * A325861 A325862 A325863

Keyword

nonn

Author

Gus Wiseman, May 31 2019

Extensions

a(21)-a(25) from Alois P. Heinz, Jun 07 2019

a(26)-a(35) from Fausto A. C. Cariboni, Oct 04 2020

Status

approved