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

%I A326496 #24 May 10 2025 14:41:08
%S A326496 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 A326496 282,282,322,322,553,553,615,689,1247,1365,1870,1870,3566,3758,5244,
%U A326496 5244,8677,8677,9807,12147,23351,23351,27469,31694,45718,47186,54594,54594,95382,108198
%N A326496 Number of maximal product-free subsets of {1..n}.
%C A326496 A set is product-free if it contains no product of two (not necessarily distinct) elements.
%C A326496 Also the number of maximal quotient-free subsets of {1..n}.
%H A326496 Fausto A. C. Cariboni, <a href="/A326496/b326496.txt">Table of n, a(n) for n = 0..85</a>
%H A326496 P. J. Cameron and P. Erdős, <a href="https://www.researchgate.net/publication/247043302_On_the_number_of_sets_of_integers_with_various_properties">On the number of integers with various properties</a>, in R. A. Mullin, ed., Number Theory: Proc. First Conf. of Canad. Number Theory Assoc. Conf., Banff, De Gruyter, Berlin, 1990, pp. 61-79.
%H A326496 Andrew Howroyd, <a href="/A326496/a326496_1.txt">PARI Program</a>
%e A326496 The a(2) = 1 through a(10) = 6 subsets (A = 10):
%e A326496   {2}  {23}  {23}  {235}  {235}   {2357}   {23578}   {23578}   {23578}
%e A326496              {34}  {345}  {256}   {2567}   {25678}   {256789}  {2378A}
%e A326496                           {3456}  {34567}  {345678}  {345678}  {256789}
%e A326496                                                      {456789}  {26789A}
%e A326496                                                                {345678A}
%e A326496                                                                {456789A}
%t A326496 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326496 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Times@@@Tuples[#,2]]=={}&]]],{n,0,10}]
%o A326496 (PARI) \\ See link for program file.
%o A326496 for(n=0, 30, print1(A326496(n), ", ")) \\ _Andrew Howroyd_, Aug 30 2019
%Y A326496 Product-free subsets are A326489.
%Y A326496 Subsets without products of distinct elements are A326117.
%Y A326496 Maximal sum-free subsets are A121269.
%Y A326496 Maximal sum-free and product-free subsets are A326497.
%Y A326496 Maximal subsets without products of distinct elements are A325710.
%Y A326496 Cf. A007865, A051026, A326076, A326491, A326492, A326495, A327591.
%K A326496 nonn
%O A326496 0,5
%A A326496 _Gus Wiseman_, Jul 09 2019
%E A326496 a(18)-a(55) from _Andrew Howroyd_, Aug 30 2019