login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299757 Weight of the strict integer partition with FDH number n. 35
0, 1, 2, 3, 4, 3, 5, 4, 6, 5, 7, 5, 8, 6, 6, 9, 10, 7, 11, 7, 7, 8, 12, 6, 13, 9, 8, 8, 14, 7, 15, 10, 9, 11, 9, 9, 16, 12, 10, 8, 17, 8, 18, 10, 10, 13, 19, 11, 20, 14, 12, 11, 21, 9, 11, 9, 13, 15, 22, 9, 23, 16, 11, 12, 12, 10, 24, 13, 14, 10, 25, 10, 26, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive integer n has a unique factorization of the form n = f(s_1)*...*f(s_k) where the s_i are strictly increasing positive integers. This determines a unique strict integer partition (s_k...s_1) whose FDH number is then defined to be n.

In analogy with the Heinz number correspondence between integer partitions and positive integers (see A056239), FDH numbers give a correspondence between strict integer partitions and positive integers.

LINKS

Table of n, a(n) for n=1..74.

EXAMPLE

Sequence of strict integer partitions begins: () (1) (2) (3) (4) (2,1) (5) (3,1) (6) (4,1) (7) (3,2) (8) (5,1) (4,2) (9).

MATHEMATICA

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)]]]]];

nn=200; FDprimeList=Array[FDfactor, nn, 1, Union];

FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];

Table[Total[FDfactor[n]/.FDrules], {n, nn}]

CROSSREFS

Cf. A004111, A050376, A056239, A061775, A064547, A106400, A213925,  A215366, A246867, A279065, A279614, A299090, A299755, A299756, A299758, A299759.

Sequence in context: A075850 A054437 A287821 * A159630 A305747 A304736

Adjacent sequences:  A299754 A299755 A299756 * A299758 A299759 A299760

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 18 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)