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A316265 FDH numbers of strict integer partitions with prime parts. 2
1, 3, 4, 7, 11, 12, 19, 21, 25, 28, 33, 41, 44, 47, 57, 61, 75, 76, 77, 83, 84, 97, 100, 121, 123, 132, 133, 139, 141, 151, 164, 169, 175, 183, 188, 197, 209, 228, 231, 233, 241, 244, 249, 271, 275, 287, 289, 291, 300, 307, 308, 329, 332, 347, 361, 363, 388 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..57.

EXAMPLE

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

   1: ()

   3: (2)

   4: (3)

   7: (5)

  11: (7)

  12: (3,2)

  19: (11)

  21: (5,2)

  25: (13)

  28: (5,3)

  33: (7,2)

  41: (17)

  44: (7,3)

  47: (19)

  57: (11,2)

  61: (23)

  75: (13,2)

  76: (11,3)

  77: (7,5)

  83: (29)

  84: (5,3,2)

MATHEMATICA

nn=100;

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/@(FDfactor[#]/.FDrules)&]

CROSSREFS

Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316266, A316267.

Sequence in context: A030489 A132841 A274280 * A205477 A023665 A023563

Adjacent sequences:  A316262 A316263 A316264 * A316266 A316267 A316268

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 28 2018

STATUS

approved

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Last modified October 17 19:42 EDT 2019. Contains 328128 sequences. (Running on oeis4.)