A161004 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 12.

4095, 8382465, 362706435, 8583644160, 49987791945, 742460072445, 1349525501415, 8789651619840, 21417452280315, 102325010111415, 116835129114795, 760279114183680, 611574734464785, 2762478701396505, 4427568695944485, 9000603258716160, 8771463461234565

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) = 4095 * A160960(n).

Sum_{k=1..n} a(k) ~ c * n^11, where c = (4095/11) * Product_{p prime} (1 + (p^10-1)/((p-1)*p^11)) = 723.3106628... .

Sum_{k>=1} 1/a(k) = (zeta(10)*zeta(11)/4095) * Product_{p prime} (1 - 2/p^11 + 1/p^21) = 0.0002443224366... . (End)

Mathematica

f[p_, e_] := p^(10*e - 10) * (p^11-1) / (p-1); a[1] = 4095; a[n_] := 4095 * Times @@ f @@@ FactorInteger[n]; Array[a, 25] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 4095 * prod(i = 1, #f~, (f[i, 1]^11 - 1)*f[i, 1]^(10*f[i, 2] - 10)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013668, A013669, A160960.

Sequence in context: A123868 A321557 A321551 * A022194 A069387 A359085

Adjacent sequences: A161001 A161002 A161003 * A161005 A161006 A161007

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved