A316094 - OEIS

%I #5 Jun 25 2018 22:51:31

%S 1,2,4,7,8,11,14,16,19,22,25,28,31,32,38,41,44,47,50,53,56,61,62,64,

%T 71,76,77,79,82,83,88,94,97,100,101,103,106,107,109,112,113,121,122,

%U 124,127,128,131,133,137,139,142,149,151,152,154,157,158,163,164,166

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

%C Also numbers n such that A305829(n) is odd.

%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 integer partitions with distinct odd parts begins (), (1), (3), (5), (3,1), (7), (5,1), (9), (11), (7,1), (13), (5,3), (15), (9,1), (11,1), (17), (7,3), (19), (13,1), (21), (5,3,1), (23), (15,1), (9,3), (25), (11,3), (7,5), (27), (17,1), (29), (7,3,1), (19,1), (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],OddQ[Times@@(FDfactor[#]/.FDrules)]&]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jun 24 2018