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