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A120286
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Numerator of 1/n^2 + 2/(n-1)^2 + 3/(n-2)^2 +...+ (n-1)/2^2 + n.
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2
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1, 9, 65, 725, 3899, 28763, 419017, 864669, 7981633, 3586319, 200763407, 2649665993, 34899471137, 176508049513, 356606957297, 12234391348253, 209672027529221, 4012917216669239, 15350275129353301, 15443118015171841
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OFFSET
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1,2
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COMMENTS
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p^2 divides a(p-1) for prime p>2. p divides a(p-2) for prime p>3.
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LINKS
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FORMULA
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a(n) = numerator[Sum[Sum[1/i^2,{i,1,k}],{k,1,n}]].
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MATHEMATICA
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Numerator[Table[Sum[Sum[1/i^2, {i, 1, k}], {k, 1, n}], {n, 1, 30}]]
Table[-EulerGamma + HarmonicNumber[1 + n, 2] + n*HarmonicNumber[1 + n, 2] - PolyGamma[0, 2 + n], {n, 1, 20}] // Numerator (* Vaclav Kotesovec, May 02 2024 *)
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PROG
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(Python)
from fractions import Fraction
def A120286(n): return sum(Fraction(n-i+1, i**2) for i in range(1, n+1)).numerator # Chai Wah Wu, May 01 2024
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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