A316264 - OEIS

%I #4 Jun 29 2018 11:35:09

%S 2,4,7,11,16,19,25,31,41,47,53,56,61,71,79,83,88,97,101,103,107,109,

%T 113,121,127,128,131,137,139,149,151,152,154,157,163,167,169,173,179,

%U 181,191,193,197,199,200,211,223,224,227,229,233,239,241,248,251,257

%N FDH numbers of strict integer partitions with odd length and all odd parts.

%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 Sequence of all strict odd integer partitions begins (1), (3), (5), (7), (9), (11), (13), (15), (17), (19), (21), (1,3,5), (23), (25), (27), (29), (1,3,7), (31).

%t nn=100;

%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],And[OddQ[Length[FDfactor[#]]],OddQ[Times@@(FDfactor[#]/.FDrules)]]&]

%Y Cf. A000700, A050376, A064547, A213925, A258116, A279065, A299755, A299757, A305829, A316094.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 28 2018