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 A161010 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 14. 3

%I

%S 1,8191,797161,33550336,305175781,6529545751,16148168401,137422176256,

%T 423644039001,2499694822171,3452271214393,26745019396096,

%U 25239592216021,132269647372591,243274230757741,562881233944576,619036127056621

%N a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 14.

%C 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

%D 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.

%H Álvar Ibeas, <a href="/A161010/b161010.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%F From _Álvar Ibeas_, Nov 26 2015: (Start)

%F Multiplicative with a(p^e) = p^(12e-12) * (p^13-1) / (p-1).

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

%F (End)

%p 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:

%p seq(f(n),n=1..100); # _Robert Israel_, Dec 08 2015

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

%o (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

%Y Cf. A160897.

%K nonn,mult

%O 1,2

%A _N. J. A. Sloane_, Nov 19 2009

%E Definition corrected by _Enrique Pérez Herrero_, Oct 30 2010

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)