A161117 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 14.

16383, 134193153, 13059888663, 549655154688, 4999694820123, 106973548038633, 264555442913583, 2251387513602048, 6940560290953383, 40952500271627493, 56558559305400519, 438163652766240768, 413500239275072043, 2166973632905158353, 3985561722504070803

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) = 16383 * A161010(n).

Sum_{k=1..n} a(k) ~ c * n^13, where c = (16383/13) * Product_{p prime} (1 + (p^12-1)/((p-1)*p^13)) = 2449.180042... .

Sum_{k>=1} 1/a(k) = (zeta(12)*zeta(13)/16383) * Product_{p prime} (1 - 2/p^13 + 1/p^25) = 6.1046412316...*10^(-5). (End)

Mathematica

f[p_, e_] := p^(12*e - 12) * (p^13-1) / (p-1); a[1] = 16383; a[n_] := 16383 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 16383 * prod(i = 1, #f~, (f[i, 1]^13 - 1)*f[i, 1]^(12*f[i, 2] - 12)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013670, A013671, A161010.

Sequence in context: A011564 A161025 A022530 * A069389 A069415 A212936

Adjacent sequences: A161114 A161115 A161116 * A161118 A161119 A161120

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved