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A161010 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 14. 3
1, 8191, 797161, 33550336, 305175781, 6529545751, 16148168401, 137422176256, 423644039001, 2499694822171, 3452271214393, 26745019396096, 25239592216021, 132269647372591, 243274230757741, 562881233944576, 619036127056621 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of lattices L in Z^13 such that the quotient group Z^13 / 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_13(n)/J_1(n) where J_13 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^(12e-12) * (p^13-1) / (p-1).

For squarefree n, a(n) = A000203(n^12).

(End)

MAPLE

f:= proc(n) local t; mul(t[1]^(12*t[2]-12)*(t[1]^13-1)/(t[1]-1), t = ifactors(n)[2]) end proc:

seq(f(n), n=1..100); # Robert Israel, Dec 08 2015

MATHEMATICA

b = 14; Table[Sum[MoebiusMu[n/d] d^(b - 1), {d, Divisors@ n}]/EulerPhi@ n, {n, 17}] (* Michael De Vlieger, Nov 27 2015 *)

PROG

(PARI) vector(100, n, sumdiv(n^12, d, if(ispower(d, 13), moebius(sqrtnint(d, 13))*sigma(n^12/d), 0))) \\ Altug Alkan, Nov 26 2015

CROSSREFS

Cf. A160897.

Sequence in context: A075960 A305758 A011563 * A075955 A075956 A022529

Adjacent sequences:  A161007 A161008 A161009 * A161011 A161012 A161013

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 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)