A316266 FDH numbers of strict integer partitions with prime parts and prime length.

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

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: A371464 A199981 A274347 * A179899 A085926 A071263

Adjacent sequences: A316263 A316264 A316265 * A316267 A316268 A316269

Keyword

nonn

Author

Gus Wiseman, Jun 28 2018

Status

approved