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A316266 FDH numbers of strict integer partitions with prime parts and prime length. 2
12, 21, 28, 33, 44, 57, 75, 76, 77, 84, 100, 123, 132, 133, 141, 164, 175, 183, 188, 209, 228, 231, 244, 249, 275, 287, 291, 300, 308, 329, 332, 363, 388, 399, 417, 427, 451, 453, 475, 484, 492, 507, 517, 525, 532, 556, 564, 581, 591, 604, 627, 671, 676, 679 (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..54.

EXAMPLE

Sequence of strict integer partitions with prime parts and prime length, preceded by their FDH numbers, begins:

  12: (3,2)

  21: (5,2)

  28: (5,3)

  33: (7,2)

  44: (7,3)

  57: (11,2)

  75: (13,2)

  76: (11,3)

  77: (7,5)

  84: (5,3,2)

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], And[PrimeQ[Length[FDfactor[#]]], And@@PrimeQ/@(FDfactor[#]/.FDrules)]&]

CROSSREFS

Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316265, A316267.

Sequence in context: A327297 A199981 A274347 * A179899 A085926 A071263

Adjacent sequences:  A316263 A316264 A316265 * A316267 A316268 A316269

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 28 2018

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)