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.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved