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A326497 Number of maximal sum-free and product-free subsets of {1..n}. 9
1, 1, 1, 1, 2, 3, 4, 6, 8, 9, 15, 21, 26, 38, 51, 69, 89, 119, 149, 197, 261, 356, 447, 601, 781, 1003, 1293, 1714, 2228, 2931, 3697, 4843, 6258, 8187, 10273, 13445, 16894, 21953, 27469, 35842, 45410 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A set is sum-free and product-free if it contains no sum or product of two (not necessarily distinct) elements.

LINKS

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

Andrew Howroyd, PARI Program

EXAMPLE

The a(2) = 1 through a(10) = 15 subsets (A = 10):

  {2}  {23}  {23}  {23}   {23}   {237}   {256}   {267}    {23A}

             {34}  {25}   {256}  {256}   {258}   {345}    {345}

                   {345}  {345}  {267}   {267}   {357}    {34A}

                          {456}  {345}   {345}   {2378}   {357}

                                 {357}   {357}   {2569}   {38A}

                                 {4567}  {2378}  {2589}   {2378}

                                         {4567}  {4567}   {2569}

                                         {5678}  {4679}   {2589}

                                                 {56789}  {267A}

                                                          {269A}

                                                          {4567}

                                                          {4679}

                                                          {479A}

                                                          {56789}

                                                          {6789A}

MATHEMATICA

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];

Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Union[Plus@@@Tuples[#, 2], Times@@@Tuples[#, 2]]]=={}&]]], {n, 0, 10}]

PROG

(PARI) \\ See link for program file.

for(n=0, 37, print1(A326497(n), ", ")) \\ Andrew Howroyd, Aug 30 2019

CROSSREFS

Sum-free and product-free subsets are A326495.

Sum-free subsets are A007865.

Maximal sum-free subsets are A121269.

Product-free subsets are A326489.

Maximal product-free subsets are A326496.

Subsets with sums (and products) are A326083.

Cf. A051026, A103580, A325710, A326076, A326117, A326491, A326492, A326498.

Sequence in context: A018338 A018271 A073667 * A325046 A160256 A151545

Adjacent sequences:  A326494 A326495 A326496 * A326498 A326499 A326500

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

a(21)-a(40) from Andrew Howroyd, Aug 30 2019

STATUS

approved

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Last modified September 23 16:01 EDT 2020. Contains 337310 sequences. (Running on oeis4.)