A160959 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 10.

1023, 522753, 10067343, 133824768, 499511463, 5144412273, 6880289823, 34259140608, 66051837423, 255250357593, 241218048687, 1316969541888, 904033571463, 3515828099553, 4915692307383, 8770339995648, 7582212353463, 33752488923153, 18339417490383, 65344091543808

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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) = 1023*A160953(n). - R. J. Mathar, Mar 16 2016

From Amiram Eldar, Nov 08 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^9, where c = (341/3) * Product_{p prime} (1 + (p^8-1)/((p-1)*p^9)) = 220.6296374... .

Sum_{k>=1} 1/a(k) = (zeta(8)*zeta(9)/1023) * Product_{p prime} (1 - 2/p^9 + 1/p^17) = 0.0009795392562... . (End)

Mathematica

f[p_, e_] := p^(8*e - 8) * (p^9-1) / (p-1); a[1] = 1023; a[n_] := 1023 * Times @@ f @@@ FactorInteger[n]; Array[a, 25] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 1023 * prod(i = 1, #f~, (f[i, 1]^9 - 1)*f[i, 1]^(8*f[i, 2] - 8)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013666, A013667, A160953.

Sequence in context: A123867 A321555 A321549 * A022192 A069385 A069411

Adjacent sequences: A160956 A160957 A160958 * A160960 A160961 A160962

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved