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A160889 Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet convolution of A000290 and the series of absolute values of A063441. - R. J. Mathar, Jun 20 2011

REFERENCES

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.

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

FORMULA

Moebius transform of A064969. Multiplicative with a(p^e) = (p^2+p+1)*p^(2*e-2). [From Vladeta Jovovic, 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

MATHEMATICA

A160889[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(4-1)/EulerPhi[n]&] [From Enrique Pérez Herrero, Aug 22 2010]

CROSSREFS

Cf. A001615, A160891, A160893, A160895, A160897, A160908, A160953, A160957, A160960, A160972, A161010, A161025, A161139, A161167, A161213

Sequence in context: A146718 A146646 A096194 * A045463 A082221 A230460

Adjacent sequences:  A160886 A160887 A160888 * A160890 A160891 A160892

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 19 2009

EXTENSIONS

Definition corrected by Vladeta Jovovic, Nov 21 2009

Typo in Mathematica program and formula fixed by Enrique Pérez Herrero, Oct 19 2010

STATUS

approved

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Last modified November 26 16:10 EST 2014. Contains 250079 sequences.