

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
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OFFSET

2,9


COMMENTS

The (sample) standard deviation sigma of {x_1,...,x_n} is calculated from sigma^2 = 1/(n1) * 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 * (22.25)^2 + (32.25)^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



