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%I #8 Nov 09 2022 07:55:14
%S 65535,2147385345,470177777355,35182761492480,499992370589085,
%T 15406315230591285,51855240592341495,576434364292792320,
%U 2248845733577866995,16383250007092548195,27375595878265462275,252417068738007613440,279538958223203141205,1699140668489253766665
%N a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 16.
%H Amiram Eldar, <a href="/A161195/b161195.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) = 65535 * A161139(n).
%F Sum_{k=1..n} a(k) ~ c * n^15, where c = 4369 * Product_{p prime} (1 + (p^14-1)/((p-1)*p^15)) = 8491.399817... .
%F Sum_{k>=1} 1/a(k) = (zeta(14)*zeta(15)/65535) * Product_{p prime} (1 - 2/p^15 + 1/p^29) = 1.5259489736...*10^(-5). (End)
%t f[p_, e_] := p^(14*e - 14) * (p^15-1) / (p-1); a[1] = 65535; a[n_] := 65535* Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)
%o (PARI) a(n) = {my(f = factor(n)); 65535 * prod(i = 1, #f~, (f[i,1]^15 - 1)*f[i,1]^(14*f[i,2] - 14)/(f[i,1] - 1));} \\ _Amiram Eldar_, Nov 08 2022
%Y Cf. A000010, A013672, A013673, A161139.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 19 2009
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