A316361 - OEIS

%I #6 Jun 30 2018 20:40:42

%S 24,56,60,110,120,135,140,168,210,216,224,264,270,273,280,308,312,315,

%T 330,342,360,378,384,408,420,440,456,459,480,504,520,540,546,550,552,

%U 576,585,594,600,616,630,660,672,693,696,702,728,744,756,759,760,770,780

%N FDH numbers of strict integer partitions such that not every distinct subset has a different average.

%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 210 is the FDH number of (5,4,2,1), and the subsets {1,5}, and {2,4} have the same average, so 210 belongs to the data.

%t nn=1000;

%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],!UnsameQ@@Mean/@Union[Subsets[FDfactor[#]/.FDrules]]&]

%Y Cf. A050376, A064547, A108917, A213925, A275972, A299755, A299757, A301899, A301900, A316271, A316313, A316362.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 30 2018