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

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, 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, 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

Offset

2,3

Comments

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.

Links

Hans Havermann, Table of n, a(n) for n = 2..10000

Mathematica

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

Prog

(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))

Crossrefs

Sequence in context: A357328 A333749 A238949 * A317751 A106490 A349281

Adjacent sequences: A076752 A076753 A076754 * A076756 A076757 A076758

Keyword

nonn

Author

Joseph L. Pe, Nov 12 2002

Status

approved