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A160897 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8. 10
1, 127, 1093, 8128, 19531, 138811, 137257, 520192, 796797, 2480437, 1948717, 8883904, 5229043, 17431639, 21347383, 33292288, 25646167, 101193219, 49659541, 158747968, 150021901, 247487059, 154764793, 568569856, 305171875, 664088461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of lattices L in Z^7 such that the quotient group Z^7 / L is C_n. - Álvar Ibeas, Oct 30 2015

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_7(n)/J_1(n)=J_7(n)/phi(n)=A069092(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Oct 27 2010

From Álvar Ibeas, Oct 30 2015: (Start)

Multiplicative with a(p^e) = p^(6e-6) * (p^7-1) / (p-1).

For squarefree n, a(n) = A000203(n^6).

(End)

MATHEMATICA

A160897[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(8 - 1)/EulerPhi[n] &] (* Enrique Pérez Herrero, Oct 27 2010 *)

PROG

(PARI) vector(30, n, sumdiv(n^6, d, if(ispower(d, 7), moebius(sqrtnint(d, 7))*sigma(n^6/d), 0))) \\ Altug Alkan, Oct 30 2015

(PARI) a(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; f[i, 1] = p^(6*f[i, 2]-6)*(1+p+p^2+p^3+p^4+p^5+p^6); f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 12 2015

CROSSREFS

Cf. A000010, A007434, A059376, A059377, A059378, A069091, A069092, A069093, A069094, A069095, A001615, A160889, A160891, A160893, A160895, A160908, A160960, A160972, A161010, A161025, A161139, A161167, A161213, A065958, A065959, A065960. - Enrique Pérez Herrero, Oct 27 2010

Sequence in context: A196658 A077361 A225148 * A038994 A068023 A194257

Adjacent sequences:  A160894 A160895 A160896 * A160898 A160899 A160900

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 19 2009

EXTENSIONS

Definition corrected by Enrique Pérez Herrero, Oct 27 2010

STATUS

approved

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Last modified February 10 18:55 EST 2016. Contains 268157 sequences.