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A319829 FDH numbers of strict integer partitions of odd numbers.

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%I A319829 #5 Sep 29 2018 12:58:10
%S A319829 2,4,6,7,10,11,12,16,18,19,20,21,25,26,30,31,33,34,35,36,41,46,47,48,
%T A319829 52,53,54,55,56,57,58,60,61,63,68,71,74,75,78,79,80,83,86,88,90,91,92,
%U A319829 93,95,97,98,99,102,103,105,108,109,116,118,119,121,123,125
%N A319829 FDH numbers of strict integer partitions of odd numbers.
%C A319829 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 A319829 The sequence of all strict integer partitions of odd numbers begins: (1), (3), (2,1), (5), (4,1), (7), (3,2), (9), (6,1), (11), (4,3), (5,2), (13), (8,1), (4,2,1), (15), (7,2), (10,1), (5,4), (6,3), (17), (12,1), (19), (9,2), (8,3), (21), (6,2,1), (7,4), (5,3,1), (11,2), (14,1), (4,3,2).
%t A319829 nn=200;
%t A319829 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 A319829 FDprimeList=Array[FDfactor,nn,1,Union];FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t A319829 Select[Range[nn],OddQ[Total[FDfactor[#]/.FDrules]]&]
%Y A319829 Complement of A319828.
%Y A319829 Cf. A050376, A064547, A213925, A299755, A299757, A300061, A300063, A319241, A319242, A319827.
%K A319829 nonn
%O A319829 1,1
%A A319829 _Gus Wiseman_, Sep 28 2018