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

Author

Gus Wiseman, Jun 06 2019

Keywords

• nonn

Comments

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

Examples

			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}
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

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