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A326076 Number of subsets of {1..n} containing all of their integer products <= n. 19
1, 2, 4, 8, 12, 24, 44, 88, 152, 232, 444, 888, 1576, 3152, 6136, 11480, 17112, 34224, 63504, 127008, 232352, 442208, 876944, 1753888, 3138848, 4895328, 9739152, 18141840, 34044720, 68089440, 123846624, 247693248, 469397440, 924014144, 1845676384, 3469128224, 5182711584 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The strict case is A326081.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

a(n) = 2*A326114(n) for n > 0. - Andrew Howroyd, Aug 30 2019

EXAMPLE

The a(0) = 1 through a(4) = 12 sets:

  {}  {}   {}     {}       {}

      {1}  {1}    {1}      {1}

           {2}    {2}      {3}

           {1,2}  {3}      {4}

                  {1,2}    {1,3}

                  {1,3}    {1,4}

                  {2,3}    {2,4}

                  {1,2,3}  {3,4}

                           {1,2,4}

                           {1,3,4}

                           {2,3,4}

                           {1,2,3,4}

The a(6) = 44 sets:

  {}  {1}  {1,3}  {1,2,4}  {1,2,4,5}  {1,2,3,4,6}  {1,2,3,4,5,6}

      {3}  {1,4}  {1,3,4}  {1,2,4,6}  {1,2,4,5,6}

      {4}  {1,5}  {1,3,5}  {1,3,4,5}  {1,3,4,5,6}

      {5}  {1,6}  {1,3,6}  {1,3,4,6}  {2,3,4,5,6}

      {6}  {2,4}  {1,4,5}  {1,3,5,6}

           {3,4}  {1,4,6}  {1,4,5,6}

           {3,5}  {1,5,6}  {2,3,4,6}

           {3,6}  {2,4,5}  {2,4,5,6}

           {4,5}  {2,4,6}  {3,4,5,6}

           {4,6}  {3,4,5}

           {5,6}  {3,4,6}

                  {3,5,6}

                  {4,5,6}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Times@@@Tuples[#, 2], #<=n&]]&]], {n, 0, 10}]

PROG

(PARI)

a(n)={

    my(lim=vector(n, k, sqrtint(k)));

    my(accept(b, k)=for(i=2, lim[k], if(k%i ==0 && bittest(b, i) && bittest(b, k/i), return(0))); 1);

    my(recurse(k, b)=

      my(m=1);

      for(j=max(2*k, n\2+1), min(2*k+1, n), if(accept(b, j), m*=2));

      k++;

      m*if(k > n\2, 1, self()(k, b + (1<<k)) + if(accept(b, k), self()(k, b)))

   );

   recurse(0, 0);

} \\ Andrew Howroyd, Aug 30 2019

CROSSREFS

Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326078, A326079, A326081.

Sequence in context: A089821 A294067 A279312 * A181808 A097942 A004653

Adjacent sequences:  A326073 A326074 A326075 * A326077 A326078 A326079

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 05 2019

EXTENSIONS

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

Terms a(31) and beyond from Andrew Howroyd, Aug 30 2019

STATUS

approved

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