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A316266 FDH numbers of strict integer partitions with prime parts and prime length.

%I A316266 #5 Jun 29 2018 11:35:25
%S A316266 12,21,28,33,44,57,75,76,77,84,100,123,132,133,141,164,175,183,188,
%T A316266 209,228,231,244,249,275,287,291,300,308,329,332,363,388,399,417,427,
%U A316266 451,453,475,484,492,507,517,525,532,556,564,581,591,604,627,671,676,679
%N A316266 FDH numbers of strict integer partitions with prime parts and prime length.
%C A316266 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 A316266 Sequence of strict integer partitions with prime parts and prime length, preceded by their FDH numbers, begins:
%e A316266   12: (3,2)
%e A316266   21: (5,2)
%e A316266   28: (5,3)
%e A316266   33: (7,2)
%e A316266   44: (7,3)
%e A316266   57: (11,2)
%e A316266   75: (13,2)
%e A316266   76: (11,3)
%e A316266   77: (7,5)
%e A316266   84: (5,3,2)
%t A316266 nn=1000;
%t A316266 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 A316266 FDprimeList=Array[FDfactor,nn,1,Union];FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t A316266 Select[Range[nn],And[PrimeQ[Length[FDfactor[#]]],And@@PrimeQ/@(FDfactor[#]/.FDrules)]&]
%Y A316266 Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316265, A316267.
%K A316266 nonn
%O A316266 1,1
%A A316266 _Gus Wiseman_, Jun 28 2018