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 A325710 Number of maximal subsets of {1..n} containing no products of distinct elements. 6
 1, 1, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 24, 28, 32, 32, 62, 62, 92, 102, 184, 184, 254, 254, 474, 506, 686, 686, 1172, 1172, 1792, 1906, 3568, 3794, 5326, 5326, 10282, 10618, 14822, 14822, 25564, 25564, 35304, 39432, 76888, 76888, 100574, 100574, 197870, 201622, 282014 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, PARI Program EXAMPLE The a(1) = 1 through a(9) = 6 maximal subsets:   {1}  {1}  {1}   {1}    {1}     {1}     {1}      {1}       {1}        {2}  {23}  {234}  {2345}  {2345}  {23457}  {23457}   {234579}                                  {2456}  {24567}  {23578}   {235789}                                  {3456}  {34567}  {24567}   {245679}                                                   {25678}   {256789}                                                   {345678}  {3456789} MATHEMATICA fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Times@@@Subsets[#, {2, n}]]=={}&]]], {n, 0, 10}] PROG (PARI) \\ See link for program file. for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019 CROSSREFS Subsets without products of distinct elements are A326117. Maximal product-free subsets are A326496. Subsets with products are A326076. Maximal subsets without sums of distinct elements are A326498. Maximal subsets without quotients are A326492. Maximal subsets without sums or products of distinct elements are A326025. Cf. A121269, A151897, A326116, A326489, A326497, A326024. Sequence in context: A071809 A324762 A104976 * A214927 A326115 A239485 Adjacent sequences:  A325707 A325708 A325709 * A325711 A325712 A325713 KEYWORD nonn AUTHOR Gus Wiseman, Jul 09 2019 EXTENSIONS Terms a(16) and beyond from Andrew Howroyd, Aug 29 2019 STATUS approved

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Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)