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A076755 Nearest integer to the kurtosis excess of the divisors of n. 1


%S 1,1,2,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,3,2,2,1,4,2,2,2,3,1,4,1,3,2,2,2,

%T 4,1,2,2,4,1,4,1,3,4,2,1,5,2,3,2,3,1,4,2,4,2,2,1,6,1,2,4,3,2,4,1,3,2,

%U 4,1,6,1,2,3,3,2,4,1,5,3,2,1,6,2,2,2,4,1,6,2,3,2,2,2,6,1,3,4,4,1,4,1,4,5,2

%N Nearest integer to the kurtosis excess of the divisors of n.

%C Kurtosis measures the concentration of data around the peak and in the tails versus the concentration in the flanks and is defined to be the fourth central moment divided by the square of the variance.

%H Hans Havermann, <a href="/A076755/b076755.txt">Table of n, a(n) for n = 2..10000</a>

%t Table[Round[Kurtosis[Divisors[n]]], {n, 2, 150}]

%o (PARI) a(n)=local(s0,s1,s2,s3,s4); s0=numdiv(n); s1=sigma(n); s2=sigma(n,2); s3=sigma(n,3); s4=sigma(n,4); if(n<2,0,round(-3+s0^2*(s4*s0-4*s3*s1+3*s2^2)/(s0*s2 -s1^2)^2))

%K nonn

%O 2,3

%A _Joseph L. Pe_, Nov 12 2002

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)