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

%I

%S 1023,522753,10067343,133824768,499511463,5144412273,6880289823,

%T 34259140608,66051837423,255250357593,241218048687,1316969541888,

%U 904033571463,3515828099553,4915692307383,8770339995648,7582212353463,33752488923153,18339417490383,65344091543808

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

%H Amiram Eldar, <a href="/A160959/b160959.txt">Table of n, a(n) for n = 1..10000</a>

%H Jin Ho Kwak and Jaeun Lee, <a href="https://doi.org/10.1142/9789812799890_0005">Enumeration of graph coverings, surface branched coverings and related group theory</a>, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134.

%F a(n) = 1023*A160953(n). - _R. J. Mathar_, Mar 16 2016

%F From _Amiram Eldar_, Nov 08 2022: (Start)

%F 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... .

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

%t 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 *)

%o (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

%Y Cf. A000010, A013666, A013667, A160953.

%K nonn

%O 1,1

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

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Last modified December 6 09:52 EST 2022. Contains 358617 sequences. (Running on oeis4.)