A326023 Number of subsets of {1..n} containing all of their integer quotients.

1, 2, 3, 5, 9, 17, 25, 49, 73, 145, 217, 433, 553, 1105, 1657, 2593, 3937, 7873, 10057, 20113, 26689, 42321, 63481, 126961, 154801, 309601, 464401, 737569, 992161, 1984321, 2450881, 4901761, 6292801, 10197313, 15295969, 26241697, 32947489, 65894977, 98842465, 161587873, 205842529

Offset

0,2

Comments

These are sets that are closed under taking the quotient of two (not necessarily distinct) divisible terms.

Links

Table of n, a(n) for n=0..40.

Formula

For n > 0, a(n) = A326078(n) + 1.

Example

The a(0) = 1 through a(5) = 17 subsets:
  {}  {}   {}     {}       {}         {}
      {1}  {1}    {1}      {1}        {1}
           {1,2}  {1,2}    {1,2}      {1,2}
                  {1,3}    {1,3}      {1,3}
                  {1,2,3}  {1,4}      {1,4}
                           {1,2,3}    {1,5}
                           {1,2,4}    {1,2,3}
                           {1,3,4}    {1,2,4}
                           {1,2,3,4}  {1,2,5}
                                      {1,3,4}
                                      {1,3,5}
                                      {1,4,5}
                                      {1,2,3,4}
                                      {1,2,3,5}
                                      {1,2,4,5}
                                      {1,3,4,5}
                                      {1,2,3,4,5}

Mathematica

Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Divide@@@Tuples[#, 2], IntegerQ]]&]], {n, 0, 10}]

Crossrefs

Cf. A007865, A051026, A054519, A067992, A103580, A325853, A325854, A325860, A325861, A325994, A326078.

Sequence in context: A154223 A061031 A339512 * A326117 A319380 A213709

Adjacent sequences: A326020 A326021 A326022 * A326024 A326025 A326026

Keyword

nonn

Author

Gus Wiseman, Jun 04 2019

Extensions

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

Status

approved