

A160908


a(n) = Sum_{dn} Moebius(n/d)*d^(b1)/phi(n) for b = 9.


3



1, 255, 3280, 32640, 97656, 836400, 960800, 4177920, 7173360, 24902280, 21435888, 107059200, 67977560, 245004000, 320311680, 534773760, 435984840, 1829206800, 943531280, 3187491840, 3151424000, 5466151440, 3559590240, 13703577600
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OFFSET

1,2


COMMENTS

a(n) = J_8(n)/J_1(n) = J_8(n)/phi(n) = A069093(n)/A000010(n), where J_k is the kth Jordan Totient Function.  Enrique Pérez Herrero, Oct 28 2010
a(n) is the number of lattices L in Z^8 such that the quotient group Z^8 / L is C_n.  Álvar Ibeas, Oct 30 2015


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
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. 97161. See p. 134.
Index to Jordan function ratios J_k/J_1


FORMULA

From Álvar Ibeas, Oct 30 2015: (Start)
Multiplicative with a(p^e) = p^(7e7) * (p^81) / (p1).
For squarefree n, a(n) = A000203(n^7).
(End)


MATHEMATICA

A160908[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(91)/EulerPhi[n]&] (* Enrique Pérez Herrero, Oct 28 2010 *)


PROG

(PARI) vector(30, n, sumdiv(n^7, d, if(ispower(d, 8), moebius(sqrtnint(d, 8))*sigma(n^7/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^(7*f[i, 2]7)*(p^81)/(p1); f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 12 2015


CROSSREFS

Sequence in context: A259247 A204738 A206048 * A038995 A068024 A028524
Adjacent sequences: A160905 A160906 A160907 * A160909 A160910 A160911


KEYWORD

nonn,mult


AUTHOR

N. J. A. Sloane, Nov 19 2009


EXTENSIONS

Definition corrected by Enrique Pérez Herrero, Oct 28 2010


STATUS

approved



