|
%I #22 Nov 01 2020 03:03:42
%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 Fausto A. C. Cariboni, <a href="/A326496/b326496.txt">Table of n, a(n) for n = 0..85</a>
%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 a(18)-a(55) from _Andrew Howroyd_, Aug 30 2019
|
