OFFSET
1,1
COMMENTS
A strict integer partition is knapsack if every subset has a different sum.
Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1,...,y_k) is f(y_1)*...*f(y_k).
EXAMPLE
a(1) = 24 is the FDH number of (3,2,1), which is not knapsack because 3 = 2 + 1.
MATHEMATICA
nn=1000;
sksQ[ptn_]:=And[UnsameQ@@ptn, UnsameQ@@Plus@@@Union[Subsets[ptn]]];
FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];
FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], !sksQ[FDfactor[#]/.FDrules]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 28 2018
STATUS
approved