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A076755
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Nearest integer to the kurtosis excess of the divisors of n.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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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.
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MATHEMATICA
| << Statistics`DescriptiveStatistics` Table[Round[Kurtosis[Divisors[n]]], {n, 2, 150}]
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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))
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CROSSREFS
| Sequence in context: A163109 A128428 A056171 * A106490 A122375 A038548
Adjacent sequences: A076752 A076753 A076754 * A076756 A076757 A076758
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Nov 12 2002
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