A326491 Number of maximal subsets of {1..n} containing no differences or quotients of pairs of distinct elements.

1, 1, 2, 2, 3, 4, 5, 7, 9, 10, 16, 22, 27, 39, 52, 70, 90, 120, 150, 198, 262, 357, 448, 602, 782, 1004, 1294, 1715, 2229, 2932, 3698, 4844, 6259, 8188, 10274, 13446, 16895, 21954, 27470, 35843, 45411

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = A326497(n) + 1 for n > 1. - Andrew Howroyd, Aug 30 2019

Example

The a(1) = 1 through a(9) = 10 subsets:
  {1}  {1}  {1}    {1}    {1}      {1}      {1}        {1}        {1}
       {2}  {2,3}  {2,3}  {2,3}    {2,3}    {2,3,7}    {2,5,6}    {2,6,7}
                   {3,4}  {2,5}    {2,5,6}  {2,5,6}    {2,5,8}    {3,4,5}
                          {3,4,5}  {3,4,5}  {2,6,7}    {2,6,7}    {3,5,7}
                                   {4,5,6}  {3,4,5}    {3,4,5}    {2,3,7,8}
                                            {3,5,7}    {3,5,7}    {2,5,6,9}
                                            {4,5,6,7}  {2,3,7,8}  {2,5,8,9}
                                                       {4,5,6,7}  {4,5,6,7}
                                                       {5,6,7,8}  {4,6,7,9}
                                                                  {5,6,7,8,9}

Mathematica

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

Crossrefs

Subsets without differences or quotients are A326490.

Subsets with differences and quotients are A326494.

Maximal subsets without differences are A121269

Maximal subsets without quotients are A326492.

Cf. A007865, A051026, A054519, A326023, A326117, A326489, A326496, A327591.

Sequence in context: A152305 A131419 A317177 * A266748 A304883 A280663

Adjacent sequences: A326488 A326489 A326490 * A326492 A326493 A326494

Keyword

nonn,more

Author

Gus Wiseman, Jul 09 2019

Extensions

a(16)-a(40) from Andrew Howroyd, Aug 30 2019

Status

approved