A161157 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 15.

32767, 536821761, 78361756228, 4397643866112, 49998474112902, 1283800652283324, 3703889238001736, 36025498551189504, 124933950274693644, 819125001391673466, 1244326279702202508, 10516894943504990208, 10751334335850714158, 60680817386182440888

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

From Amiram Eldar, Nov 08 2022: (Start)

a(n) = 32767 * A161025(n).

Sum_{k=1..n} a(k) ~ c * n^14, where c = (4681/2) * Product_{p prime} (1 + (p^13-1)/((p-1)*p^14)) = 4548.801953... .

Sum_{k>=1} 1/a(k) = (zeta(13)*zeta(14)/32767) * Product_{p prime} (1 - 2/p^14 + 1/p^27) = 3.05203853014...*10^(-5). (End)

Mathematica

f[p_, e_] := p^(13*e - 13) * (p^14-1) / (p-1); a[1] = 32767; a[n_] := 32767 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 32767 * prod(i = 1, #f~, (f[i, 1]^14 - 1)*f[i, 1]^(13*f[i, 2] - 13)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013671, A013672, A161025.

Sequence in context: A075961 A075962 A022531 * A069390 A069416 A289478

Adjacent sequences: A161154 A161155 A161156 * A161158 A161159 A161160

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved