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

0,3

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}

Links

Table of n, a(n) for n=0..37.

Formula

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

Example

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.

Sequence in context: A283834 A341582 A370648 * A135231 A326489 A217356

Adjacent sequences: A326111 A326112 A326113 * A326115 A326116 A326117

Keyword

nonn

Author

Gus Wiseman, Jun 06 2019

Extensions

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

Status

approved