A160898 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 7.

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

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