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%I #4 Jun 29 2018 11:35:46
%S 24,40,70,84,120,126,135,168,198,210,216,220,231,264,270,280,286,312,
%T 330,351,360,364,378,384,408,416,420,440,456,462,504,520,528,540,544,
%U 546,552,560,576,594,600,616,630,640,646,660,663,680,696,702,728,744,748
%N FDH numbers of strict non-knapsack partitions.
%C A strict integer partition is knapsack if every subset has a different sum.
%C 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).
%e a(1) = 24 is the FDH number of (3,2,1), which is not knapsack because 3 = 2 + 1.
%t nn=1000;
%t sksQ[ptn_]:=And[UnsameQ@@ptn,UnsameQ@@Plus@@@Union[Subsets[ptn]]];
%t 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)]]]]];
%t FDprimeList=Array[FDfactor,nn,1,Union];FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t Select[Range[nn],!sksQ[FDfactor[#]/.FDrules]&]
%Y Cf. A000712, A005117, A050376, A056239, A064547, A108917, A213925, A275972, A284640, A299702, A299755, A299757, A301899, A301900.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jun 28 2018
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