A325869 Number of maximal subsets of {1..n} containing n such that every pair of distinct elements has a different quotient.

1, 1, 1, 2, 3, 4, 6, 6, 6, 20, 32, 29, 57, 83, 113, 183, 373, 233, 549, 360

Offset

1,4

Links

Table of n, a(n) for n=1..20.

Example

The a(1) = 1 through a(7) = 6 subsets:
  {1}  {1,2}  {1,2,3}  {1,3,4}  {1,2,3,5}  {1,2,5,6}    {1,2,3,5,7}
                       {2,3,4}  {1,3,4,5}  {2,3,5,6}    {1,2,5,6,7}
                                {2,3,4,5}  {2,4,5,6}    {2,3,4,5,7}
                                           {1,3,4,5,6}  {2,3,5,6,7}
                                                        {2,4,5,6,7}
                                                        {1,3,4,5,6,7}

Mathematica

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&)/@y];
Table[Length[fasmax[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Divide@@@Subsets[#, {2}]&]]], {n, 10}]

Crossrefs

Cf. A025582, A067992, A108917, A143823, A196723, A196724.

Cf. A325853, A325854, A325858, A325860, A325861, A325864, A325868.

Sequence in context: A240809 A214322 A075527 * A154257 A336406 A297351

Adjacent sequences: A325866 A325867 A325868 * A325870 A325871 A325872

Keyword

nonn,more

Author

Gus Wiseman, Jun 02 2019

Status

approved