A319828 FDH numbers of strict integer partitions of even numbers.

1, 3, 5, 8, 9, 13, 14, 15, 17, 22, 23, 24, 27, 28, 29, 32, 37, 38, 39, 40, 42, 43, 44, 45, 49, 50, 51, 59, 62, 64, 65, 66, 67, 69, 70, 72, 73, 76, 77, 81, 82, 84, 85, 87, 89, 94, 96, 100, 101, 104, 106, 107, 110, 111, 112, 113, 114, 115, 117, 120, 122, 124

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..62.

Example

The sequence of all strict integer partitions of even numbers begins: (), (2), (4), (3,1), (6), (8), (5,1), (4,2), (10), (7,1), (12), (3,2,1), (6,2), (5,3), (14), (9,1), (16).

Mathematica

nn=200;
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], EvenQ[Total[FDfactor[#]/.FDrules]]&]

Crossrefs

Complement of A319827.

Cf. A050376, A064547, A213925, A299755, A299757, A300061, A300063, A319241, A319242, A319829.

Sequence in context: A081451 A107605 A109314 * A325540 A102529 A186621

Adjacent sequences: A319825 A319826 A319827 * A319829 A319830 A319831

Keyword

nonn

Author

Gus Wiseman, Sep 28 2018

Status

approved