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%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