A316361 FDH numbers of strict integer partitions such that not every distinct subset has a different average.

24, 56, 60, 110, 120, 135, 140, 168, 210, 216, 224, 264, 270, 273, 280, 308, 312, 315, 330, 342, 360, 378, 384, 408, 420, 440, 456, 459, 480, 504, 520, 540, 546, 550, 552, 576, 585, 594, 600, 616, 630, 660, 672, 693, 696, 702, 728, 744, 756, 759, 760, 770, 780

Offset: 1

Author

Gus Wiseman, Jun 30 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

			210 is the FDH number of (5,4,2,1), and the subsets {1,5}, and {2,4} have the same average, so 210 belongs to the data.
		

Crossrefs

Cf. A050376, A064547, A108917, A213925, A275972, A299755, A299757, A301899, A301900, A316271, A316313, A316362.

Programs

Mathematica

nn=1000;
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],!UnsameQ@@Mean/@Union[Subsets[FDfactor[#]/.FDrules]]&]