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A326490 Number of subsets of {1..n} containing no differences or quotients of pairs of distinct elements. 5
1, 2, 3, 5, 7, 12, 18, 31, 46, 72, 102, 172, 259, 428, 607, 989, 1329, 2142, 3117, 4953, 6956, 11032, 15321, 23979, 33380, 48699, 66849, 104853, 144712, 220758, 304133, 461580, 636556, 973843, 1316513, 1958828, 2585433, 3882843, 5237093, 7884277, 10555739, 15729293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..41.

FORMULA

For n > 0, a(n) = A326495(n) + 1.

EXAMPLE

The a(0) = 1 through a(6) = 18 subsets:

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

      {1}  {1}  {1}    {1}    {1}      {1}

           {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}

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

                                       {4,5}

                                       {4,6}

                                       {5,6}

                                       {2,5,6}

                                       {3,4,5}

                                       {4,5,6}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], Intersection[#, Union[Divide@@@Reverse/@Subsets[#, {2}], Subtract@@@Reverse/@Subsets[#, {2}]]]=={}&]], {n, 0, 10}]

PROG

(PARI)

a(n)={

   my(recurse(k, b)=

    if(k > n, 1,

      my(t = self()(k + 1, b));

      for(i=1, k\2, if(bittest(b, i) && (bittest(b, k-i) || (!(k%i) && bittest(b, k/i))), return(t)));

      t += self()(k + 1, b + (1<<k));

      t);

   );

   if(n, recurse(2, 0)) + 1;

} \\ Andrew Howroyd, Aug 25 2019

CROSSREFS

Subsets without difference are A007865.

Maximal subsets without differences or quotients are A326491.

Subsets without quotients are A327591.

Subsets with differences and quotients are A326494.

Cf. A051026, A054519, A325860, A326023, A326079, A326489.

Sequence in context: A169986 A218021 A137713 * A191385 A335093 A143642

Adjacent sequences:  A326487 A326488 A326489 * A326491 A326492 A326493

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

Terms a(19) and beyond from Andrew Howroyd, Aug 25 2019

STATUS

approved

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)