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A316361 FDH numbers of strict integer partitions such that not every distinct subset has a different average. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A003756 A135191 A216697 * A277108 A039375 A043198

Adjacent sequences:  A316358 A316359 A316360 * A316362 A316363 A316364

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 30 2018

STATUS

approved

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)