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A326497 Number of maximal sum-free and product-free subsets of {1..n}.

%I A326497 #20 Oct 28 2020 04:06:43
%S A326497 1,1,1,1,2,3,4,6,8,9,15,21,26,38,51,69,89,119,149,197,261,356,447,601,
%T A326497 781,1003,1293,1714,2228,2931,3697,4843,6258,8187,10273,13445,16894,
%U A326497 21953,27469,35842,45410,58948,73939,95199,120593,154510,192995,247966,312642
%N A326497 Number of maximal sum-free and product-free subsets of {1..n}.
%C A326497 A set is sum-free and product-free if it contains no sum or product of two (not necessarily distinct) elements.
%H A326497 Fausto A. C. Cariboni, <a href="/A326497/b326497.txt">Table of n, a(n) for n = 0..68</a>
%H A326497 Andrew Howroyd, <a href="/A326497/a326497.txt">PARI Program</a>
%e A326497 The a(2) = 1 through a(10) = 15 subsets (A = 10):
%e A326497   {2}  {23}  {23}  {23}   {23}   {237}   {256}   {267}    {23A}
%e A326497              {34}  {25}   {256}  {256}   {258}   {345}    {345}
%e A326497                    {345}  {345}  {267}   {267}   {357}    {34A}
%e A326497                           {456}  {345}   {345}   {2378}   {357}
%e A326497                                  {357}   {357}   {2569}   {38A}
%e A326497                                  {4567}  {2378}  {2589}   {2378}
%e A326497                                          {4567}  {4567}   {2569}
%e A326497                                          {5678}  {4679}   {2589}
%e A326497                                                  {56789}  {267A}
%e A326497                                                           {269A}
%e A326497                                                           {4567}
%e A326497                                                           {4679}
%e A326497                                                           {479A}
%e A326497                                                           {56789}
%e A326497                                                           {6789A}
%t A326497 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326497 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Tuples[#,2],Times@@@Tuples[#,2]]]=={}&]]],{n,0,10}]
%o A326497 (PARI) \\ See link for program file.
%o A326497 for(n=0, 37, print1(A326497(n), ", ")) \\ _Andrew Howroyd_, Aug 30 2019
%Y A326497 Sum-free and product-free subsets are A326495.
%Y A326497 Sum-free subsets are A007865.
%Y A326497 Maximal sum-free subsets are A121269.
%Y A326497 Product-free subsets are A326489.
%Y A326497 Maximal product-free subsets are A326496.
%Y A326497 Subsets with sums (and products) are A326083.
%Y A326497 Cf. A051026, A103580, A325710, A326076, A326117, A326491, A326492, A326498.
%K A326497 nonn
%O A326497 0,5
%A A326497 _Gus Wiseman_, Jul 09 2019
%E A326497 a(21)-a(40) from _Andrew Howroyd_, Aug 30 2019
%E A326497 a(41)-a(48) from _Jinyuan Wang_, Oct 11 2020