A308542 Number of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.

1, 2, 4, 8, 16, 28, 56, 100, 200, 364, 728, 1184, 2368, 4448, 8056, 15008, 30016, 52736, 105472, 183424, 339840, 663616, 1327232, 2217088, 4434176, 8744320, 16559168, 30034624, 60069248, 103402112, 206804224, 379941440, 730800064, 1454649248, 2659869664, 4786282208

Offset: 1

Author

Gus Wiseman, Jun 06 2019

Keywords

• nonn

Comments

First differs from A326116 at a(12) = 1184, A326116(12) = 1232.

If this sequence counts product-closed sets, A326116 counts product-free sets.

Examples

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

Crossrefs

Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A326117.

Programs

Mathematica

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

Formula

For n > 0, a(n) = A326081(n)/2.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Aug 24 2019