A325859 - OEIS

A325859

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

1, 1, 1, 1, 1, 1, 4, 4, 11, 11, 28, 28, 60, 60, 140, 241, 299, 299, 572, 572, 971

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OFFSET

0,7

LINKS

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.

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved