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A319829 FDH numbers of strict integer partitions of odd numbers. 1
2, 4, 6, 7, 10, 11, 12, 16, 18, 19, 20, 21, 25, 26, 30, 31, 33, 34, 35, 36, 41, 46, 47, 48, 52, 53, 54, 55, 56, 57, 58, 60, 61, 63, 68, 71, 74, 75, 78, 79, 80, 83, 86, 88, 90, 91, 92, 93, 95, 97, 98, 99, 102, 103, 105, 108, 109, 116, 118, 119, 121, 123, 125 (list; graph; refs; listen; history; text; internal format)
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..63.

EXAMPLE

The sequence of all strict integer partitions of odd numbers begins: (1), (3), (2,1), (5), (4,1), (7), (3,2), (9), (6,1), (11), (4,3), (5,2), (13), (8,1), (4,2,1), (15), (7,2), (10,1), (5,4), (6,3), (17), (12,1), (19), (9,2), (8,3), (21), (6,2,1), (7,4), (5,3,1), (11,2), (14,1), (4,3,2).

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], OddQ[Total[FDfactor[#]/.FDrules]]&]

CROSSREFS

Complement of A319828.

Cf. A050376, A064547, A213925, A299755, A299757, A300061, A300063, A319241, A319242, A319827.

Sequence in context: A259983 A050095 A102528 * A272631 A002158 A274431

Adjacent sequences:  A319826 A319827 A319828 * A319830 A319831 A319832

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 28 2018

STATUS

approved

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Last modified April 25 13:31 EDT 2019. Contains 322461 sequences. (Running on oeis4.)