A325869 - OEIS

%I #4 Jun 02 2019 23:39:58

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

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

%e The a(1) = 1 through a(7) = 6 subsets:

%e   {1}  {1,2}  {1,2,3}  {1,3,4}  {1,2,3,5}  {1,2,5,6}    {1,2,3,5,7}

%e                        {2,3,4}  {1,3,4,5}  {2,3,5,6}    {1,2,5,6,7}

%e                                 {2,3,4,5}  {2,4,5,6}    {2,3,4,5,7}

%e                                            {1,3,4,5,6}  {2,3,5,6,7}

%e                                                         {2,4,5,6,7}

%e                                                         {1,3,4,5,6,7}

%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&)/@y];

%t Table[Length[fasmax[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Divide@@@Subsets[#,{2}]&]]],{n,10}]

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

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

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Jun 02 2019