A326117 Number of subsets of {1..n} containing no products of two or more distinct elements.

1, 2, 3, 5, 9, 17, 29, 57, 101, 201, 365, 729, 1233, 2465, 4593, 8297, 15921, 31841, 55953, 111905, 195713, 362337, 697361, 1394721, 2334113, 4668225, 9095393, 17225313, 31242785, 62485569, 106668609, 213337217, 392606529, 755131841, 1491146913, 2727555425, 4947175713

Offset

0,2

Comments

If this sequence counts product-free sets, A326081 counts product-closed sets.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..47

Formula

For n > 0, a(n) = A326116(n) + 1.

Example

The a(6) = 28 sets:
  {}  {1}  {2,3}  {2,3,4}  {2,3,4,5}
      {2}  {2,4}  {2,3,5}  {2,4,5,6}
      {3}  {2,5}  {2,4,5}  {3,4,5,6}
      {4}  {2,6}  {2,4,6}
      {5}  {3,4}  {2,5,6}
      {6}  {3,5}  {3,4,5}
           {3,6}  {3,4,6}
           {4,5}  {3,5,6}
           {4,6}  {4,5,6}
           {5,6}

Mathematica

Table[Length[Select[Subsets[Range[n]], Intersection[#, Select[Times@@@Subsets[#, {2}], #<=n&]]=={}&]], {n, 0, 20}]

Crossrefs

Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A308542.

Sequence in context: A061031 A339512 A326023 * A319380 A213709 A054187

Adjacent sequences: A326114 A326115 A326116 * A326118 A326119 A326120

Keyword

nonn

Author

Gus Wiseman, Jun 06 2019

Extensions

Terms a(21)-a(36) from Andrew Howroyd, Aug 30 2019

Status

approved