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 A053822 Dirichlet inverse of sigma_2 function (A001157). 4
 1, -5, -10, 4, -26, 50, -50, 0, 9, 130, -122, -40, -170, 250, 260, 0, -290, -45, -362, -104, 500, 610, -530, 0, 25, 850, 0, -200, -842, -1300, -962, 0, 1220, 1450, 1300, 36, -1370, 1810, 1700, 0, -1682, -2500, -1850, -488, -234, 2650, -2210, 0, 49, -125, 2900, -680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS sigma_2(n) is the sum of the squares of the divisors of n (A001157). REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 39. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA Dirichlet g.f.: 1/(zeta(x)zeta(x-2)) Multiplicative with a(p^1) = -1-p^2, a(p^2) = p^2, a(p^e) = 0 for e>=3. - Mitch Harris, Jun 27 2005 a(n) = Sum_{d|n} mu(n/d)*mu(d)*d^2. - Ilya Gutkovskiy, Nov 06 2018 MAPLE f1:= proc(p, e) if e = 1 then -1-p^2 elif e=2 then p^2 else 0 fi end proc: f:= n -> mul(f1(t[1], t[2]), t=ifactors(n)[2]); map(f, [\$1..100]); # Robert Israel, Jan 29 2018 MATHEMATICA a[n_] := Sum[MoebiusMu[n/d] MoebiusMu[d] d^2, {d, Divisors[n]}]; Array[a, 100] (* Jean-François Alcover, Mar 05 2019, after Ilya Gutkovskiy *) PROG (PARI) seq(n)={dirdiv(vector(n, n, n==1), vector(n, n, sigma(n, 2)))} \\ Andrew Howroyd, Aug 05 2018 CROSSREFS Cf. A001157, A046692. Sequence in context: A054513 A295121 A066200 * A262922 A276652 A137404 Adjacent sequences:  A053819 A053820 A053821 * A053823 A053824 A053825 KEYWORD sign,mult,look AUTHOR N. J. A. Sloane, Apr 08 2000 STATUS approved

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Last modified October 23 12:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)