A319827 FDH numbers of relatively prime strict integer partitions.

2, 6, 8, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 30, 32, 33, 34, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112

Offset: 1

Author

Gus Wiseman, Sep 28 2018

Keywords

• nonn

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).

Examples

			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).
		

Crossrefs

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

Programs

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