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%I #6 Jun 29 2018 11:35:18
%S 1,3,4,7,11,12,19,21,25,28,33,41,44,47,57,61,75,76,77,83,84,97,100,
%T 121,123,132,133,139,141,151,164,169,175,183,188,197,209,228,231,233,
%U 241,244,249,271,275,287,289,291,300,307,308,329,332,347,361,363,388
%N FDH numbers of strict integer partitions with prime parts.
%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 Sequence of strict integer partitions with prime parts, preceded by their FDH numbers, begins:
%e 1: ()
%e 3: (2)
%e 4: (3)
%e 7: (5)
%e 11: (7)
%e 12: (3,2)
%e 19: (11)
%e 21: (5,2)
%e 25: (13)
%e 28: (5,3)
%e 33: (7,2)
%e 41: (17)
%e 44: (7,3)
%e 47: (19)
%e 57: (11,2)
%e 61: (23)
%e 75: (13,2)
%e 76: (11,3)
%e 77: (7,5)
%e 83: (29)
%e 84: (5,3,2)
%t nn=100;
%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],And@@PrimeQ/@(FDfactor[#]/.FDrules)&]
%Y Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316266, A316267.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jun 28 2018
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