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A053825 Dirichlet inverse of sigma_3 function (A001158). 6
1, -9, -28, 8, -126, 252, -344, 0, 27, 1134, -1332, -224, -2198, 3096, 3528, 0, -4914, -243, -6860, -1008, 9632, 11988, -12168, 0, 125, 19782, 0, -2752, -24390, -31752, -29792, 0, 37296, 44226, 43344, 216, -50654, 61740, 61544, 0, -68922, -86688 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sigma_3(n) is the sum of the cubes of the divisors of n (A001158).

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 39.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

Dirichlet g.f.: 1/(zeta(x)zeta(x-3))

Multiplicative with a(p^1) = -1-p^3, a(p^2) = p^3, a(p^e) = 0 for e>=3. - Mitch Harris, Jun 27 2005

a(n) = Sum_{d|n} mu(n/d)*mu(d)*d^3. - Ilya Gutkovskiy, Nov 06 2018

PROG

(PARI) seq(n)={dirdiv(vector(n, n, n==1), vector(n, n, sigma(n, 3)))} \\ Andrew Howroyd, Aug 05 2018

CROSSREFS

Cf. A001158, A046692.

Sequence in context: A020281 A075539 A225300 * A033479 A254139 A034116

Adjacent sequences:  A053822 A053823 A053824 * A053826 A053827 A053828

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Apr 08 2000

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)