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A325859
Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different product.
15
1, 1, 1, 1, 1, 1, 4, 4, 11, 11, 28, 28, 60, 60, 140, 241, 299, 299, 572, 572, 971
OFFSET
0,7
EXAMPLE
The a(1) = 1 through a(9) = 11 subsets:
{1} {12} {123} {1234} {12345} {2356} {23567} {123457} {235678}
{12345} {123457} {123578} {1234579}
{12456} {124567} {124567} {1235789}
{13456} {134567} {125678} {1245679}
{134567} {1256789}
{134578} {1345679}
{135678} {1345789}
{145678} {1356789}
{234578} {1456789}
{235678} {2345789}
{245678} {2456789}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Times@@@Subsets[#, {2}]&]]], {n, 0, 15}]
CROSSREFS
The subset case is A196724.
The maximal case is A325859.
The integer partition case is A325856.
The strict integer partition case is A325855.
Heinz numbers of the counterexamples are given by A325993.
Sequence in context: A168373 A266438 A128499 * A265206 A327684 A231064
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved