A326492 Number of maximal subsets of {1..n} containing no quotients of pairs of distinct elements.

1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 7, 7, 10, 10, 16, 18, 31, 31, 47, 47, 52, 62, 104, 104, 130, 159, 283, 283, 323, 323, 554, 554, 616, 690, 1248, 1366, 1871, 1871, 3567, 3759, 5245, 5245, 8678, 8678, 9808, 12148, 23352, 23352, 27470, 31695, 45719, 47187, 54595, 54595, 95383, 108199

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

a(n) = A326496(n) + 1 for n > 1. - Andrew Howroyd, Aug 30 2019

Example

The a(0) = 1 through a(9) = 5 subsets:
  {}  {1}  {1}  {1}   {1}   {1}    {1}     {1}      {1}       {1}
           {2}  {23}  {23}  {235}  {235}   {2357}   {23578}   {23578}
                      {34}  {345}  {256}   {2567}   {25678}   {256789}
                                   {3456}  {34567}  {345678}  {345678}
                                                              {456789}

Mathematica

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&]]=={}&]]], {n, 0, 10}]

Crossrefs

Subsets with quotients are A326023.

Subsets with quotients > 1 are A326079.

Subsets without quotients are A327591.

Maximal subsets without differences or quotients are A326491.

Maximal subsets without quotients (or products) are A326496.

Cf. A007865, A121269, A325860, A325994, A326117, A326489, A326490.

Sequence in context: A181988 A194173 A028825 * A132924 A076890 A103358

Adjacent sequences: A326489 A326490 A326491 * A326493 A326494 A326495

Keyword

nonn

Author

Gus Wiseman, Jul 09 2019

Extensions

Terms a(16) and beyond from Andrew Howroyd, Aug 30 2019

Status

approved