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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 11.
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%I #8 Nov 09 2022 07:55:35

%S 2047,2094081,60435628,1072169472,4997558082,61825647444,96371138776,

%T 548950769664,1189554465924,5112501917886,5309390815620,

%U 31654731491328,23516361067738,98587674967848,147547904812968,281062794067968,257921219638566,1216914218640252

%N a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 11.

%H Amiram Eldar, <a href="/A160964/b160964.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 From _Amiram Eldar_, Nov 08 2022: (Start)

%F a(n) = 2047 * A160957(n).

%F Sum_{k=1..n} a(k) ~ c * n^10, where c = (2047/10) * Product_{p prime} (1 + (p^9-1)/((p-1)*p^10)) = 397.5922753... .

%F Sum_{k>=1} 1/a(k) = (zeta(9)*zeta(10)/2047) * Product_{p prime} (1 - 2/p^10 + 1/p^19) = 0.0004890150305... . (End)

%t f[p_, e_] := p^(9*e - 9) * (p^10-1) / (p-1); a[1] = 2047; a[n_] := 2047 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)

%o (PARI) a(n) = {my(f = factor(n)); 2047 * 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

%Y Cf. A000010, A013667, A013668, A160957.

%K nonn

%O 1,1

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