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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 September 10 09:32 EDT 2024. Contains 375786 sequences. (Running on oeis4.)