A319828 - OEIS

%I #7 Sep 29 2018 12:58:04

%S 1,3,5,8,9,13,14,15,17,22,23,24,27,28,29,32,37,38,39,40,42,43,44,45,

%T 49,50,51,59,62,64,65,66,67,69,70,72,73,76,77,81,82,84,85,87,89,94,96,

%U 100,101,104,106,107,110,111,112,113,114,115,117,120,122,124

%N FDH numbers of strict integer partitions of even numbers.

%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 The sequence of all strict integer partitions of even numbers begins: (), (2), (4), (3,1), (6), (8), (5,1), (4,2), (10), (7,1), (12), (3,2,1), (6,2), (5,3), (14), (9,1), (16).

%t nn=200;

%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],EvenQ[Total[FDfactor[#]/.FDrules]]&]

%Y Complement of A319827.

%Y Cf. A050376, A064547, A213925, A299755, A299757, A300061, A300063, A319241, A319242, A319829.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 28 2018