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A325861
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Number of maximal subsets of {1..n} such that every pair of distinct elements has a different quotient.
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15
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1, 1, 1, 1, 3, 3, 6, 6, 9, 13, 32, 32, 57, 57, 140, 229, 373, 373, 549, 549, 825
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OFFSET
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0,5
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LINKS
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EXAMPLE
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The a(1) = 1 through a(9) = 13 subsets:
{1} {12} {123} {123} {1235} {1235} {12357} {23457} {24567}
{134} {1345} {1256} {12567} {24567} {123578}
{234} {2345} {2345} {23457} {123578} {134567}
{2356} {23567} {125678} {134578}
{2456} {24567} {134567} {135678}
{13456} {134567} {134578} {145678}
{135678} {145789}
{145678} {234579}
{235678} {235678}
{235789}
{345789}
{356789}
{1256789}
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MATHEMATICA
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fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Divide@@@Subsets[#, {2}]&]]], {n, 0, 10}]
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CROSSREFS
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The integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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