login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067631 If n is composite then a(n) is the standard deviation of the prime factors of n, rounded off to the nearest integer (rounding up if there's a choice), with each factor counted according to its frequency of occurrence in the prime factorization. If n is 1 or prime then a(n)=0. 1
0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 4, 1, 0, 0, 1, 0, 2, 3, 6, 0, 1, 0, 8, 0, 3, 0, 2, 0, 0, 6, 11, 1, 1, 0, 12, 7, 2, 0, 3, 0, 5, 1, 15, 0, 0, 0, 2, 10, 6, 0, 1, 4, 3, 11, 19, 0, 1, 0, 21, 2, 0, 6, 5, 0, 9, 14, 3, 0, 1, 0, 25, 1, 10, 3, 6, 0, 1, 0, 28, 0, 2, 8, 29, 18, 5, 0, 1, 4, 12, 20, 32, 10, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,9

COMMENTS

The (sample) standard deviation sigma of {x_1,...,x_n} is calculated from sigma^2 = 1/(n-1) * sum_{1,...,n}(x_i - mu)^2, where mu denotes the average of {x_1,...,x_n}.

LINKS

Table of n, a(n) for n=2..97.

EXAMPLE

24 = 2^3 * 3^1, so the corresponding average = (2 + 2 + 2 + 3)/ 4 = 2.25 and the standard deviation is [(1/3){3 * (2-2.25)^2 + (3-2.25)^2}]^0.5 = 0.5, which rounds to 1. So a(24) = 1.

MATHEMATICA

<<Statistics`NormalDistribution` f[n_] := Flatten[Table[ #[[1]], {#[[2]]}]&/@FactorInteger[n]]; a[n_] := If[PrimeQ[n]||n==1, 0, Floor[StandardDeviation[f[n]]+1/2]]

CROSSREFS

Sequence in context: A110109 A145973 A155761 * A134317 A123641 A217377

Adjacent sequences:  A067628 A067629 A067630 * A067632 A067633 A067634

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Feb 02 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 05 2002

Edited by Dean Hickerson, Feb 12 2002

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 24 01:27 EDT 2021. Contains 347617 sequences. (Running on oeis4.)