A319827 - OEIS

%I #4 Sep 29 2018 12:57:57

%S 2,6,8,10,12,14,18,20,21,22,24,26,28,30,32,33,34,35,38,40,42,44,46,48,

%T 50,52,54,55,56,57,58,60,62,63,66,68,70,72,74,75,76,77,78,80,82,84,86,

%U 88,90,91,93,94,95,96,98,99,100,102,104,105,106,108,110,112

%N FDH numbers of relatively prime strict integer partitions.

%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 relatively prime strict integer partitions begins: (1), (2,1), (3,1), (4,1), (3,2), (5,1), (6,1), (4,3), (5,2), (7,1), (3,2,1), (8,1), (5,3), (4,2,1).

%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],GCD@@(FDfactor[#]/.FDrules)==1&]

%Y Cf. A050376, A056239, A064547, A213925, A289508, A289509, A290103, A299755, A299757, A319826.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 28 2018