%I #6 Jun 02 2019 00:49:45
%S 1,1,1,1,1,1,4,4,11,11,28,28,60,60,140,241,299,299,572,572,971
%N Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different product.
%e The a(1) = 1 through a(9) = 11 subsets:
%e {1} {12} {123} {1234} {12345} {2356} {23567} {123457} {235678}
%e {12345} {123457} {123578} {1234579}
%e {12456} {124567} {124567} {1235789}
%e {13456} {134567} {125678} {1245679}
%e {134567} {1256789}
%e {134578} {1345679}
%e {135678} {1345789}
%e {145678} {1356789}
%e {234578} {1456789}
%e {235678} {2345789}
%e {245678} {2456789}
%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t Table[Length[fasmax[Select[Subsets[Range[n]],UnsameQ@@Times@@@Subsets[#,{2}]&]]],{n,0,15}]
%Y The subset case is A196724.
%Y The maximal case is A325859.
%Y The integer partition case is A325856.
%Y The strict integer partition case is A325855.
%Y Heinz numbers of the counterexamples are given by A325993.
%Y Cf. A002033, A108917, A143823, A275972, A325858, A325860, A325861, A325869, A325878, A325879, A325880.
%K nonn,more
%O 0,7
%A _Gus Wiseman_, May 31 2019