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%I #11 Nov 09 2022 07:56:59
%S 255,32385,278715,2072640,4980405,35396805,35000535,132648960,
%T 203183235,632511435,496922835,2265395520,1333405965,4445067945,
%U 5443582665,8489533440,6539772585,25804270845,12663182955,40480731840,38255584755,63109200045,39465022215,144985313280
%N a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 8.
%H Amiram Eldar, <a href="/A160913/b160913.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) = 255*A160897(n). - _R. J. Mathar_, Mar 15 2016
%F From _Amiram Eldar_, Nov 08 2022: (Start)
%F Sum_{k=1..n} a(k) ~ c * n^7, where c = (255/7) * Product_{p prime} (1 + (p^6-1)/((p-1)*p^7)) = 70.419647503... .
%F Sum_{k>=1} 1/a(k) = (zeta(6)*zeta(7)/255) * Product_{p prime} (1 - 2/p^7 + 1/p^13) = 0.003956793297... . (End)
%t f[p_, e_] := p^(6*e - 6) * (p^7-1) / (p-1); a[1] = 255; a[n_] := 255 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)
%o (PARI) a(n) = {my(f = factor(n)); 255 * prod(i = 1, #f~, (f[i,1]^7 - 1)*f[i,1]^(6*f[i,2] - 6)/(f[i,1] - 1));} \\ _Amiram Eldar_, Nov 08 2022
%Y Cf. A000010, A013664, A013665, A160897.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 19 2009
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