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 A053826 Dirichlet inverse of sigma_4 function (A001159). 5
 1, -17, -82, 16, -626, 1394, -2402, 0, 81, 10642, -14642, -1312, -28562, 40834, 51332, 0, -83522, -1377, -130322, -10016, 196964, 248914, -279842, 0, 625, 485554, 0, -38432, -707282, -872644, -923522, 0, 1200644, 1419874, 1503652, 1296, -1874162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS sigma_4(n) is the sum of the 4th powers of the divisors of n (A001159). REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 39. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 FORMULA Dirichlet g.f.: 1/(zeta(x)zeta(x-4)) Multiplicative with a(p^1) = -1 - p^4, a(p^2) = p^4, a(p^e) = 0 for e>=3. - Mitch Harris, Jun 27 2005 a(n) = Sum_{d|n} mu(n/d)*mu(d)*d^4. - Ilya Gutkovskiy, Nov 06 2018 MATHEMATICA Table[DivisorSum[n, MoebiusMu[n/#]*MoebiusMu[#]*#^4  &], {n, 1, 50}] (* G. C. Greubel, Nov 07 2018 *) PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*moebius(d)*d^4); \\ Michel Marcus, Nov 06 2018 CROSSREFS Cf. A001159, A046099 (where a(n)=0). Sequence in context: A044204 A044585 A197397 * A184982 A088687 A321560 Adjacent sequences:  A053823 A053824 A053825 * A053827 A053828 A053829 KEYWORD sign,mult AUTHOR N. J. A. Sloane, Apr 08 2000 STATUS approved

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Last modified July 20 14:21 EDT 2019. Contains 325185 sequences. (Running on oeis4.)