A161195 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 16.

65535, 2147385345, 470177777355, 35182761492480, 499992370589085, 15406315230591285, 51855240592341495, 576434364292792320, 2248845733577866995, 16383250007092548195, 27375595878265462275, 252417068738007613440, 279538958223203141205, 1699140668489253766665

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) = 65535 * A161139(n).

Sum_{k=1..n} a(k) ~ c * n^15, where c = 4369 * Product_{p prime} (1 + (p^14-1)/((p-1)*p^15)) = 8491.399817... .

Sum_{k>=1} 1/a(k) = (zeta(14)*zeta(15)/65535) * Product_{p prime} (1 - 2/p^15 + 1/p^29) = 1.5259489736...*10^(-5). (End)

Mathematica

f[p_, e_] := p^(14*e - 14) * (p^15-1) / (p-1); a[1] = 65535; a[n_] := 65535* Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 65535 * prod(i = 1, #f~, (f[i, 1]^15 - 1)*f[i, 1]^(14*f[i, 2] - 14)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013672, A013673, A161139.

Sequence in context: A011566 A161167 A022532 * A069391 A188096 A188105

Adjacent sequences: A161192 A161193 A161194 * A161196 A161197 A161198

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved