A161215 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 17.

131071, 8589737985, 2821088318560, 281468534292480, 4999961852994576, 184880022956829600, 725978907114673600, 9223160931695984640, 40479533921803813920, 327672500035999538160, 602267704294826658336, 6058148592249392332800, 7268068365187380400720

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) = 131071 * A161167(n).

Sum_{k=1..n} a(k) ~ c * n^16, where c = (131071/16) * Product_{p prime} (1 + (p^15-1)/((p-1)*p^16)) = 15921.65841... .

Sum_{k>=1} 1/a(k) = (zeta(15)*zeta(16)/131071) * Product_{p prime} (1 - 2/p^16 + 1/p^31) = 7.6295695155...*10^(-6). (End)

Mathematica

f[p_, e_] := p^(15*e - 15) * (p^16-1) / (p-1); a[1] = 131071; a[n_] := 131071 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 131071 * prod(i = 1, #f~, (f[i, 1]^16 - 1)*f[i, 1]^(15*f[i, 2] - 15)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013673, A013674, A161167.

Sequence in context: A075967 A075968 A022533 * A069392 A289479 A222529

Adjacent sequences: A161212 A161213 A161214 * A161216 A161217 A161218

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved