The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326076 Number of subsets of {1..n} containing all of their integer products <= n. 19
 1, 2, 4, 8, 12, 24, 44, 88, 152, 232, 444, 888, 1576, 3152, 6136, 11480, 17112, 34224, 63504, 127008, 232352, 442208, 876944, 1753888, 3138848, 4895328, 9739152, 18141840, 34044720, 68089440, 123846624, 247693248, 469397440, 924014144, 1845676384, 3469128224, 5182711584 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The strict case is A326081. LINKS FORMULA a(n) = 2*A326114(n) for n > 0. - Andrew Howroyd, Aug 30 2019 EXAMPLE The a(0) = 1 through a(4) = 12 sets:   {}  {}   {}     {}       {}       {1}  {1}    {1}      {1}            {2}    {2}      {3}            {1,2}  {3}      {4}                   {1,2}    {1,3}                   {1,3}    {1,4}                   {2,3}    {2,4}                   {1,2,3}  {3,4}                            {1,2,4}                            {1,3,4}                            {2,3,4}                            {1,2,3,4} The a(6) = 44 sets:   {}  {1}  {1,3}  {1,2,4}  {1,2,4,5}  {1,2,3,4,6}  {1,2,3,4,5,6}       {3}  {1,4}  {1,3,4}  {1,2,4,6}  {1,2,4,5,6}       {4}  {1,5}  {1,3,5}  {1,3,4,5}  {1,3,4,5,6}       {5}  {1,6}  {1,3,6}  {1,3,4,6}  {2,3,4,5,6}       {6}  {2,4}  {1,4,5}  {1,3,5,6}            {3,4}  {1,4,6}  {1,4,5,6}            {3,5}  {1,5,6}  {2,3,4,6}            {3,6}  {2,4,5}  {2,4,5,6}            {4,5}  {2,4,6}  {3,4,5,6}            {4,6}  {3,4,5}            {5,6}  {3,4,6}                   {3,5,6}                   {4,5,6} MATHEMATICA Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Times@@@Tuples[#, 2], #<=n&]]&]], {n, 0, 10}] PROG (PARI) a(n)={     my(lim=vector(n, k, sqrtint(k)));     my(accept(b, k)=for(i=2, lim[k], if(k%i ==0 && bittest(b, i) && bittest(b, k/i), return(0))); 1);     my(recurse(k, b)=       my(m=1);       for(j=max(2*k, n\2+1), min(2*k+1, n), if(accept(b, j), m*=2));       k++;       m*if(k > n\2, 1, self()(k, b + (1<

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)