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

1,1

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).

Links

Table of n, a(n) for n=1..53.

Example

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.

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]]&]

Crossrefs

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

Sequence in context: A135191 A216697 A332541 * A277108 A039375 A043198

Adjacent sequences: A316358 A316359 A316360 * A316362 A316363 A316364

Keyword

nonn

Author

Gus Wiseman, Jun 30 2018

Status

approved