login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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