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A160957 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11. 4
1, 1023, 29524, 523776, 2441406, 30203052, 47079208, 268173312, 581120892, 2497558338, 2593742460, 15463962624, 11488207654, 48162029784, 72080070744, 137304735744, 125999618778, 594486672516, 340614792100, 1278749869056 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the number of lattices L in Z^10 such that the quotient group Z^10 / L is C_n. - Álvar Ibeas, Nov 26 2015
LINKS
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) = A069095(n)/A000010(n). - R. J. Mathar, Jul 12 2011
From Álvar Ibeas, Nov 26 2015: (Start)
Multiplicative with a(p^e) = p^(9e-9) * (p^10-1) / (p-1).
For squarefree n, a(n) = A000203(n^9). (End)
From Amiram Eldar, Nov 08 2022: (Start)
Sum_{k=1..n} a(k) ~ c * n^10, where c = (1/10) * Product_{p prime} (1 + (p^9-1)/((p-1)*p^10)) = 0.1942316928... .
Sum_{k>=1} 1/a(k) = zeta(9)*zeta(10) * Product_{p prime} (1 - 2/p^10 + 1/p^19) = 1.0010137674... . (End)
MATHEMATICA
b = 11; Table[Sum[MoebiusMu[n/d] d^(b - 1)/EulerPhi@ n, {d, Divisors@ n}], {n, 20}] (* Michael De Vlieger, Nov 27 2015 *)
f[p_, e_] := p^(9*e - 9) * (p^10-1) / (p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 25] (* Amiram Eldar, Nov 08 2022 *)
PROG
(PARI) vector(100, n, sumdiv(n^9, d, if(ispower(d, 10), moebius(sqrtnint(d, 10))*sigma(n^9/d), 0))) \\ Altug Alkan, Nov 26 2015
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^10 - 1)*f[i, 1]^(9*f[i, 2] - 9)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022
CROSSREFS
Column 10 of A263950.
Sequence in context: A023060 A223079 A011560 * A038997 A068026 A075946
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 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)