A326495 Number of subsets of {1..n} containing no sums or products of pairs of elements.

1, 1, 2, 4, 6, 11, 17, 30, 45, 71, 101, 171, 258, 427, 606, 988, 1328, 2141, 3116, 4952, 6955, 11031, 15320, 23978, 33379, 48698, 66848, 104852, 144711, 220757, 304132, 461579, 636555, 973842, 1316512, 1958827, 2585432, 3882842, 5237092, 7884276, 10555738, 15729292

Offset: 0

Author

Gus Wiseman, Jul 09 2019

Keywords

• nonn

Comments

The pairs are not required to be strict.

Examples

			The a(1) = 1 through a(6) = 17 subsets:
  {}  {}   {}     {}     {}       {}
      {2}  {2}    {2}    {2}      {2}
           {3}    {3}    {3}      {3}
           {2,3}  {4}    {4}      {4}
                  {2,3}  {5}      {5}
                  {3,4}  {2,3}    {6}
                         {2,5}    {2,3}
                         {3,4}    {2,5}
                         {3,5}    {2,6}
                         {4,5}    {3,4}
                         {3,4,5}  {3,5}
                                  {4,5}
                                  {4,6}
                                  {5,6}
                                  {2,5,6}
                                  {3,4,5}
                                  {4,5,6}
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..90

Crossrefs

Subsets without sums are A007865.

Subsets without products are A326489.

Subsets without differences or quotients are A326490.

Maximal subsets without sums or products are A326497.

Subsets with sums (and products) are A326083.

Cf. A051026, A103580, A326020, A326076, A326117, A326491.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Tuples[#,2],Times@@@Tuples[#,2]]]=={}&]],{n,0,10}]

Formula

For n > 0, a(n) = A326490(n) - 1.

Extensions

a(19)-a(41) from Andrew Howroyd, Aug 25 2019