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A160893 a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n). 8
1, 31, 121, 496, 781, 3751, 2801, 7936, 9801, 24211, 16105, 60016, 30941, 86831, 94501, 126976, 88741, 303831, 137561, 387376, 338921, 499255, 292561, 960256, 488125, 959171, 793881, 1389296, 732541, 2929531, 954305, 2031616, 1948705 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

a(n) = J_5(n)/J_1(n) = J_5(n)/phi(n) = A059378(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Oct 19 2010

Multiplicative with a(p^e) = p^(4e-4)*(1 + p+ p^2 + p^3 + p^4). - R. J. Mathar, Jul 10 2011

MAPLE

A160893 := proc(n) a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*p^(4*e-4)*(1+p+p^2+p^3+p^4) ; end do; a; end proc: # R. J. Mathar, Jul 10 2011

MATHEMATICA

A160893[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(6-1)/EulerPhi[n]&] (* Enrique Pérez Herrero, Oct 19 2010 *)

PROG

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d^5/eulerphi(n)); \\ Michel Marcus, Feb 15 2015

CROSSREFS

Cf. A160891, A160895, A160897, A160960, A160972, A161010, A161025, A161139 , A161167, A161213, A065958, A065959, A065960. - Enrique Pérez Herrero, Oct 19 2010

Sequence in context: A256650 A131550 A158558 * A202994 A038992 A068021

Adjacent sequences:  A160890 A160891 A160892 * A160894 A160895 A160896

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 19 2009

EXTENSIONS

Definition corrected by Enrique Pérez Herrero, Oct 19 2010

STATUS

approved

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Last modified August 3 17:30 EDT 2015. Contains 260264 sequences.