A316264 FDH numbers of strict integer partitions with odd length and all odd parts.

2, 4, 7, 11, 16, 19, 25, 31, 41, 47, 53, 56, 61, 71, 79, 83, 88, 97, 101, 103, 107, 109, 113, 121, 127, 128, 131, 137, 139, 149, 151, 152, 154, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 200, 211, 223, 224, 227, 229, 233, 239, 241, 248, 251, 257

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..56.

Example

Sequence of all strict odd integer partitions begins (1), (3), (5), (7), (9), (11), (13), (15), (17), (19), (21), (1,3,5), (23), (25), (27), (29), (1,3,7), (31).

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[OddQ[Length[FDfactor[#]]], OddQ[Times@@(FDfactor[#]/.FDrules)]]&]

Crossrefs

Cf. A000700, A050376, A064547, A213925, A258116, A279065, A299755, A299757, A305829, A316094.

Sequence in context: A261993 A299251 A238485 * A067744 A307601 A194215

Adjacent sequences: A316261 A316262 A316263 * A316265 A316266 A316267

Keyword

nonn

Author

Gus Wiseman, Jun 28 2018

Status

approved