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%I #14 Nov 09 2022 07:56:45
%S 31,465,1240,3720,4836,18600,12400,29760,33480,72540,45384,148800,
%T 73780,186000,193440,238080,161820,502200,224440,580320,496000,680760,
%U 394320,1190400,604500,1106700,903960,1488000,783060,2901600,954304,1904640,1815360,2427300
%N a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 5.
%H Amiram Eldar, <a href="/A160894/b160894.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) = 31*A160891(n). - _R. J. Mathar_, Mar 16 2016
%F From _Amiram Eldar_, Nov 08 2022: (Start)
%F Sum_{k=1..n} a(k) ~ c * n^4, where c = (31/4) * Product_{p prime} (1 + 1/p^2 + 1/p^3 + 1/p^4) = 14.3522727306... .
%F Sum_{k>=1} 1/a(k) = (zeta(3)*zeta(4)/31) * Product_{p prime} (1 - 2/p^4 + 1/p^7) = 0.03599754726... . (End)
%t f[p_, e_] := p^(3 e - 3)*(1 + p + p^2 + p^3); a[1] = 31; a[n_] := 31 * Times @@ f @@@ FactorInteger[n]; Array[a, 32] (* _Amiram Eldar_, Nov 08 2022 *)
%o (PARI) a(n) = {my(f = factor(n)); 31 * prod(i = 1, #f~, (f[i,1]^3 + f[i,1]^2 + f[i,1] + 1)*f[i,1]^(3*f[i,2] - 3));} \\ _Amiram Eldar_, Nov 08 2022
%Y Cf. A000010, A002117, A013662, A160891.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 19 2009
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