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A160972 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 13. 3
1, 4095, 265720, 8386560, 61035156, 1088123400, 2306881200, 17175674880, 47071500840, 249938963820, 313842837672, 2228476723200, 1941507093540, 9446678514000, 16218261652320, 35175782154240, 36413889826860 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of lattices L in Z^12 such that the quotient group Z^12 / L is C_n. - Álvar Ibeas, Nov 26 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

Álvar Ibeas, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = J_12(n)/J_1(n) where J_12 and J_1(n) = A000010(n) are Jordan functions. - R. J. Mathar, Jul 12 2011

From Álvar Ibeas, Nov 26 2015: (Start)

Multiplicative with a(p^e) = p^(11e-11) * (p^12-1) / (p-1).

For squarefree n, a(n) = A000203(n^11).

(End)

MATHEMATICA

b = 13; Table[Sum[MoebiusMu[n/d] d^(b - 1)/EulerPhi@ n, {d, Divisors@ n}], {n, 17}] (* Michael De Vlieger, Nov 27 2015 *)

PROG

(PARI) vector(100, n, sumdiv(n^11, d, if(ispower(d, 12), moebius(sqrtnint(d, 12))*sigma(n^11/d), 0))) \\ Altug Alkan, Nov 26 2015

CROSSREFS

Sequence in context: A075957 A075953 A011562 * A038999 A022528 A024010

Adjacent sequences:  A160969 A160970 A160971 * A160973 A160974 A160975

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 19 2009

EXTENSIONS

Definition corrected by Enrique Pérez Herrero, Oct 30 2010

STATUS

approved

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Last modified March 23 12:18 EDT 2017. Contains 283951 sequences.