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A088838
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Numerator of the quotient sigma(3n)/sigma(n).
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8
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4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 121, 4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 121, 4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 40, 4, 4, 13, 4, 4, 13, 4, 4, 364, 4, 4, 13, 4, 4, 13, 4, 4, 40
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (3^(k+2)-1)*(x^(3^k)+x^(2*3^k))/(2*(1-x^(3^(k+1)))). (End)
a(n) = sigma(3*n)/(sigma(3*n) - 3*sigma(n)), where sigma(n) = A000203(n). - Peter Bala, Jun 10 2022
Sum_{k=1..n} a(k) ~ (3/log(3))*n*log(n) + (1/2 + 3*(gamma-1)/log(3))*n, where gamma is Euler's constant (A001620).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A080278(k) = 4*A214369 + 1 = 3.728614... . (End)
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MAPLE
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numtheory[sigma](3*n)/numtheory[sigma](n) ;
numer(%) ;
end proc:
seq((3^(2+padic:-ordp(n, 3))-1)/2, n=1..100); # Robert Israel, Nov 19 2017
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MATHEMATICA
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k=3; Table[Numerator[DivisorSigma[1, k*n]/DivisorSigma[1, n]], {n, 1, 128}]
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PROG
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(PARI) a(n) = numerator(sigma(3*n)/sigma(n)) \\ Felix Fröhlich, Nov 19 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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