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 A053825 Dirichlet inverse of sigma_3 function (A001158). 6

%I

%S 1,-9,-28,8,-126,252,-344,0,27,1134,-1332,-224,-2198,3096,3528,0,

%T -4914,-243,-6860,-1008,9632,11988,-12168,0,125,19782,0,-2752,-24390,

%U -31752,-29792,0,37296,44226,43344,216,-50654,61740,61544,0,-68922,-86688

%N Dirichlet inverse of sigma_3 function (A001158).

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

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

%H Andrew Howroyd, <a href="/A053825/b053825.txt">Table of n, a(n) for n = 1..1000</a>

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

%F 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

%F a(n) = Sum_{d|n} mu(n/d)*mu(d)*d^3. - _Ilya Gutkovskiy_, Nov 06 2018

%o (PARI) seq(n)={dirdiv(vector(n, n, n==1), vector(n, n, sigma(n, 3)))} \\ _Andrew Howroyd_, Aug 05 2018

%Y Cf. A001158, A046692.

%K sign,mult

%O 1,2

%A _N. J. A. Sloane_, Apr 08 2000

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)