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A325859 Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different product. 12

%I

%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

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)