A326114 Number of subsets of {2..n} containing no product of two or more (not necessarily distinct) elements.

1, 1, 2, 4, 6, 12, 22, 44, 76, 116, 222, 444, 788, 1576, 3068, 5740, 8556, 17112, 31752, 63504, 116176, 221104, 438472, 876944, 1569424, 2447664, 4869576, 9070920, 17022360, 34044720, 61923312, 123846624, 234698720, 462007072, 922838192, 1734564112, 2591355792, 5182711584

Offset: 0

Author

Gus Wiseman, Jun 06 2019

Keywords

• nonn

Comments

The strict case is A326117.

Also the number of subsets of {2..n} containing all of their integer products <= n. For example, the a(1) = 1 through a(5) = 12 subsets are:

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

{2} {2} {3} {3}

{3} {4} {4}

{2,3} {2,4} {5}

{3,4} {2,4}

{2,3,4} {3,4}

{3,5}

{4,5}

{2,3,4}

{2,4,5}

{3,4,5}

{2,3,4,5}

Examples

			The a(1) = 1 through a(5) = 12 subsets:
  {}  {}   {}     {}     {}
      {2}  {2}    {2}    {2}
           {3}    {3}    {3}
           {2,3}  {4}    {4}
                  {2,3}  {5}
                  {3,4}  {2,3}
                         {2,5}
                         {3,4}
                         {3,5}
                         {4,5}
                         {2,3,5}
                         {3,4,5}
		

Crossrefs

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

Formula

a(n > 0) = A326076(n)/2.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Aug 30 2019