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%I #5 Jun 02 2019 00:49:57
%S 1,1,1,1,3,3,6,6,9,13,32,32,57,57,140,229,373,373,549,549,825
%N Number of maximal subsets of {1..n} such that every pair of distinct elements has a different quotient.
%e The a(1) = 1 through a(9) = 13 subsets:
%e {1} {12} {123} {123} {1235} {1235} {12357} {23457} {24567}
%e {134} {1345} {1256} {12567} {24567} {123578}
%e {234} {2345} {2345} {23457} {123578} {134567}
%e {2356} {23567} {125678} {134578}
%e {2456} {24567} {134567} {135678}
%e {13456} {134567} {134578} {145678}
%e {135678} {145789}
%e {145678} {234579}
%e {235678} {235678}
%e {235789}
%e {345789}
%e {356789}
%e {1256789}
%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t Table[Length[fasmax[Select[Subsets[Range[n]],UnsameQ@@Divide@@@Subsets[#,{2}]&]]],{n,0,10}]
%Y The subset case is A325860.
%Y The maximal case is A325861.
%Y The integer partition case is A325853.
%Y The strict integer partition case is A325854.
%Y Heinz numbers of the counterexamples are given by A325994.
%Y Cf. A002033, A103300, A143823, A196724, A325859, A325868, A325869.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, May 31 2019
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