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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 14.
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%I #8 Nov 09 2022 07:55:27

%S 16383,134193153,13059888663,549655154688,4999694820123,

%T 106973548038633,264555442913583,2251387513602048,6940560290953383,

%U 40952500271627493,56558559305400519,438163652766240768,413500239275072043,2166973632905158353,3985561722504070803

%N a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 14.

%H Amiram Eldar, <a href="/A161117/b161117.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) = 16383 * A161010(n).

%F Sum_{k=1..n} a(k) ~ c * n^13, where c = (16383/13) * Product_{p prime} (1 + (p^12-1)/((p-1)*p^13)) = 2449.180042... .

%F Sum_{k>=1} 1/a(k) = (zeta(12)*zeta(13)/16383) * Product_{p prime} (1 - 2/p^13 + 1/p^25) = 6.1046412316...*10^(-5). (End)

%t f[p_, e_] := p^(12*e - 12) * (p^13-1) / (p-1); a[1] = 16383; a[n_] := 16383 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)

%o (PARI) a(n) = {my(f = factor(n)); 16383 * prod(i = 1, #f~, (f[i,1]^13 - 1)*f[i,1]^(12*f[i,2] - 12)/(f[i,1] - 1));} \\ _Amiram Eldar_, Nov 08 2022

%Y Cf. A000010, A013670, A013671, A161010.

%K nonn

%O 1,1

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