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

%I A326495 #17 Oct 24 2020 02:30:50
%S A326495 1,1,2,4,6,11,17,30,45,71,101,171,258,427,606,988,1328,2141,3116,4952,
%T A326495 6955,11031,15320,23978,33379,48698,66848,104852,144711,220757,304132,
%U A326495 461579,636555,973842,1316512,1958827,2585432,3882842,5237092,7884276,10555738,15729292
%N A326495 Number of subsets of {1..n} containing no sums or products of pairs of elements.
%C A326495 The pairs are not required to be strict.
%H A326495 Fausto A. C. Cariboni, <a href="/A326495/b326495.txt">Table of n, a(n) for n = 0..90</a>
%F A326495 For n > 0, a(n) = A326490(n) - 1.
%e A326495 The a(1) = 1 through a(6) = 17 subsets:
%e A326495   {}  {}   {}     {}     {}       {}
%e A326495       {2}  {2}    {2}    {2}      {2}
%e A326495            {3}    {3}    {3}      {3}
%e A326495            {2,3}  {4}    {4}      {4}
%e A326495                   {2,3}  {5}      {5}
%e A326495                   {3,4}  {2,3}    {6}
%e A326495                          {2,5}    {2,3}
%e A326495                          {3,4}    {2,5}
%e A326495                          {3,5}    {2,6}
%e A326495                          {4,5}    {3,4}
%e A326495                          {3,4,5}  {3,5}
%e A326495                                   {4,5}
%e A326495                                   {4,6}
%e A326495                                   {5,6}
%e A326495                                   {2,5,6}
%e A326495                                   {3,4,5}
%e A326495                                   {4,5,6}
%t A326495 Table[Length[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Tuples[#,2],Times@@@Tuples[#,2]]]=={}&]],{n,0,10}]
%Y A326495 Subsets without sums are A007865.
%Y A326495 Subsets without products are A326489.
%Y A326495 Subsets without differences or quotients are A326490.
%Y A326495 Maximal subsets without sums or products are A326497.
%Y A326495 Subsets with sums (and products) are A326083.
%Y A326495 Cf. A051026, A103580, A326020, A326076, A326117, A326491.
%K A326495 nonn
%O A326495 0,3
%A A326495 _Gus Wiseman_, Jul 09 2019
%E A326495 a(19)-a(41) from _Andrew Howroyd_, Aug 25 2019