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 A326496 Number of maximal product-free subsets of {1..n}. 9

%I

%S 1,1,1,1,2,2,3,3,3,4,6,6,9,9,15,17,30,30,46,46,51,61,103,103,129,158,

%T 282,282,322,322,553,553,615,689,1247,1365,1870,1870,3566,3758,5244,

%U 5244,8677,8677,9807,12147,23351,23351,27469,31694,45718,47186,54594,54594,95382,108198

%N Number of maximal product-free subsets of {1..n}.

%C A set is product-free if it contains no product of two (not necessarily distinct) elements.

%C Also the number of maximal quotient-free subsets of {1..n}.

%H Andrew Howroyd, <a href="/A326496/a326496_1.txt">PARI Program</a>

%e The a(2) = 1 through a(10) = 6 subsets (A = 10):

%e {2} {23} {23} {235} {235} {2357} {23578} {23578} {23578}

%e {34} {345} {256} {2567} {25678} {256789} {2378A}

%e {3456} {34567} {345678} {345678} {256789}

%e {456789} {26789A}

%e {345678A}

%e {456789A}

%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];

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

%o (PARI) \\ See link for program file.

%o for(n=0, 30, print1(A326496(n), ", ")) \\ _Andrew Howroyd_, Aug 30 2019

%Y Product-free subsets are A326489.

%Y Subsets without products of distinct elements are A326117.

%Y Maximal sum-free subsets are A121269.

%Y Maximal sum-free and product-free subsets are A326497.

%Y Maximal subsets without products of distinct elements are A325710.

%Y Cf. A007865, A051026, A326076, A326491, A326492, A326495, A327591.

%K nonn

%O 0,5

%A _Gus Wiseman_, Jul 09 2019

%E Terms a(18) and beyond from _Andrew Howroyd_, Aug 30 2019

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)