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A319828
FDH numbers of strict integer partitions of even numbers.
1
1, 3, 5, 8, 9, 13, 14, 15, 17, 22, 23, 24, 27, 28, 29, 32, 37, 38, 39, 40, 42, 43, 44, 45, 49, 50, 51, 59, 62, 64, 65, 66, 67, 69, 70, 72, 73, 76, 77, 81, 82, 84, 85, 87, 89, 94, 96, 100, 101, 104, 106, 107, 110, 111, 112, 113, 114, 115, 117, 120, 122, 124
OFFSET
1,2
COMMENTS
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).
EXAMPLE
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).
MATHEMATICA
nn=200;
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)]]]]];
FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], EvenQ[Total[FDfactor[#]/.FDrules]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 28 2018
STATUS
approved