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A161213 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 18. 5
1, 131071, 64570081, 8589869056, 190734863281, 8463265086751, 38771752331201, 562945658454016, 2779530261754401, 24999809265103951, 50544702849929377, 554648540725313536, 720867993281778161, 5081852349802846271 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the number of lattices L in Z^17 such that the quotient group Z^17 / L is C_n. - Álvar Ibeas, Nov 26 2015
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
Jin Ho Kwak and Jaeun 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.
FORMULA
a(n) = J_17(n)/A000010(n), where J_17 is the 17th Jordan totient function.
From Álvar Ibeas, Nov 26 2015: (Start)
Multiplicative with a(p^e) = p^(16e-16) * (p^17-1) / (p-1).
For squarefree n, a(n) = A000203(n^16). (End)
From Amiram Eldar, Nov 08 2022: (Start)
Sum_{k=1..n} a(k) ~ c * n^17, where c = (1/17) * Product_{p prime} (1 + (p^16-1)/((p-1)*p^17)) = 0.1143286202... .
Sum_{k>=1} 1/a(k) = zeta(16)*zeta(17) * Product_{p prime} (1 - 2/p^17 + 1/p^33) = 1.000007645061593... . (End)
MAPLE
A161213 := proc(n)
add(numtheory[mobius](n/d)*d^17, d=numtheory[divisors](n)) ;
%/numtheory[phi](n) ;
end proc:
for n from 1 to 5000 do
printf("%d %d\n", n, A161213(n)) ;
end do: # R. J. Mathar, Mar 15 2016
MATHEMATICA
A161213[n_]:=DivisorSum[n, MoebiusMu[n/#]*#^(18-1)/EulerPhi[n]&]; Array[A161213, 20]
f[p_, e_] := p^(16*e - 16) * (p^17-1) / (p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)
PROG
(PARI) A161213(n)=sumdiv(n, d, moebius(n/d)*d^17)/eulerphi(n);
(PARI) vector(100, n, sumdiv(n^16, d, if(ispower(d, 17), moebius(sqrtnint(d, 16))*sigma(n^16/d), 0))) \\ Altug Alkan, Nov 26 2015
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^17 - 1)*f[i, 1]^(16*f[i, 2] - 16)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022
CROSSREFS
Column 17 of A263950.
Sequence in context: A051331 A075972 A011567 * A075967 A075968 A022533
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 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)