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A160889
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Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.
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9
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1, 7, 13, 28, 31, 91, 57, 112, 117, 217, 133, 364, 183, 399, 403, 448, 307, 819, 381, 868, 741, 931, 553, 1456, 775, 1281, 1053, 1596, 871, 2821, 993, 1792, 1729, 2149, 1767, 3276, 1407, 2667, 2379, 3472, 1723, 5187, 1893, 3724, 3627, 3871, 2257, 5824, 2793
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OFFSET
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1,2
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COMMENTS
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Dirichlet convolution of A000290 and the series of absolute values of A063441. - R. J. Mathar, Jun 20 2011
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REFERENCES
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J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134.
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LINKS
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Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
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FORMULA
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Moebius transform of A064969. Multiplicative with a(p^e) = (p^2+p+1)*p^(2*e-2). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Nov 21 2009]
a(n)=J_3(n)/J_1(n)=J_3(n)/phi(n)=A059376(n)/A000010(n), where J_k is the k-th Jordan Totient Function [From Enrique Pérez Herrero, Aug 22 2010]
Dirichlet g.f. zeta(s-2)*product_{primes p} (1+p^(1-s)+p^(-s)). - R. J. Mathar, Jun 20 2011
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MATHEMATICA
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A160889[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(4-1)/EulerPhi[n]&] [From Enrique Pérez Herrero, Aug 22 2010]
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CROSSREFS
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Cf. A001615, A160891, A160893, A160895, A160897, A160908, A160953, A160957, A160960, A160972, A161010, A161025, A161139, A161167, A161213
Sequence in context: A146718 A146646 A096194 * A045463 A082221 A182624
Adjacent sequences: A160886 A160887 A160888 * A160890 A160891 A160892
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane, Nov 19 2009
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EXTENSIONS
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Definition corrected by Vladeta Jovovic (vladeta(AT)eunet.yu), Nov 21 2009
Typo in Mathematica program and formula fixed by Enrique Pérez Herrero, Oct 19 2010
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STATUS
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approved
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