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A326489 Number of product-free subsets of {1..n}. 11
1, 1, 2, 4, 6, 12, 22, 44, 88, 136, 252, 504, 896, 1792, 3392, 6352, 9720, 19440, 35664, 71328, 129952, 247232, 477664, 955328, 1700416, 2657280, 5184000, 10368000, 19407360, 38814720, 68868352, 137736704, 260693504, 505830400, 999641600, 1882820608, 2807196672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..100

Andrew Howroyd, PARI Program

EXAMPLE

The a(0) = 1 through a(6) = 22 subsets:

  {}  {}  {}   {}     {}     {}       {}

          {2}  {2}    {2}    {2}      {2}

               {3}    {3}    {3}      {3}

               {2,3}  {4}    {4}      {4}

                      {2,3}  {5}      {5}

                      {3,4}  {2,3}    {6}

                             {2,5}    {2,3}

                             {3,4}    {2,5}

                             {3,5}    {2,6}

                             {4,5}    {3,4}

                             {2,3,5}  {3,5}

                             {3,4,5}  {3,6}

                                      {4,5}

                                      {4,6}

                                      {5,6}

                                      {2,3,5}

                                      {2,5,6}

                                      {3,4,5}

                                      {3,4,6}

                                      {3,5,6}

                                      {4,5,6}

                                      {3,4,5,6}

MATHEMATICA

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

CROSSREFS

Product-closed subsets are A326076.

Subsets containing no products are A326114.

Subsets containing no products of distinct elements are A326117.

Subsets containing no quotients are A327591.

Maximal product-free subsets are A326496.

Cf. A007865, A051026, A326023, A326081, A326116, A326495.

Sequence in context: A283834 A326114 A135231 * A217356 A030793 A085988

Adjacent sequences:  A326486 A326487 A326488 * A326490 A326491 A326492

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Aug 25 2019

a(0)=1 prepended to data, example and b-file by Peter Kagey, Sep 18 2019

STATUS

approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)