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 A160898 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 7. 1
 127, 8001, 46228, 256032, 496062, 2912364, 2490216, 8193024, 11233404, 31251906, 22498812, 93195648, 51083718, 156883608, 180566568, 262176768, 191591946, 707704452, 331934820, 1000060992, 906438624, 1417425156, 854570808, 2982260736, 1550193750, 3218274234 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Jin Ho Kwak and Jaeun Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134. FORMULA a(n) = 127*A160895(n). - R. J. Mathar, Mar 15 2016 From Amiram Eldar, Nov 08 2022: (Start) Sum_{k=1..n} a(k) ~ c * n^6, where c = (127/6) * Product_{p prime} (1 + (p^5-1)/((p-1)*p^6)) = 40.6863089361... . Sum_{k>=1} 1/a(k) = (zeta(5)*zeta(6)/127) * Product_{p prime} (1 - 2/p^6 + 1/p^11) = 0.008027649545... . (End) MATHEMATICA f[p_, e_] := p^(5*e - 5) * (p^6-1) / (p-1); a[1] = 127; a[n_] := 127 * Times @@ f @@@ FactorInteger[n]; Array[a, 25] (* Amiram Eldar, Nov 08 2022 *) PROG (PARI) a(n) = {my(f = factor(n)); 127 * prod(i = 1, #f~, (f[i, 1]^6 - 1)*f[i, 1]^(5*f[i, 2] - 5)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022 CROSSREFS Cf. A000010, A013663, A013664, A160895. Sequence in context: A137789 A268663 A005464 * A140477 A110828 A286790 Adjacent sequences: A160895 A160896 A160897 * A160899 A160900 A160901 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 19 2009 STATUS approved

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Last modified August 15 17:35 EDT 2024. Contains 375173 sequences. (Running on oeis4.)