OFFSET
1,1
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 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).
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], OddQ[Total[FDfactor[#]/.FDrules]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 28 2018
STATUS
approved