A160896 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 6.

63, 1953, 7623, 31248, 49203, 236313, 176463, 499968, 617463, 1525293, 1014615, 3781008, 1949283, 5470353, 5953563, 7999488, 5590683, 19141353, 8666343, 24404688, 21352023, 31453065, 18431343, 60496128, 30751875, 60427773, 50014503, 87525648, 46150083, 184560453

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

a(n) = 63*A160893(n). - R. J. Mathar, Mar 16 2016

From Amiram Eldar, Nov 08 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^5, where c = (63/5) * Product_{p prime} (1 + (p^4-1)/((p-1)*p^5)) = 23.9347523175... .

Sum_{k>=1} 1/a(k) = (zeta(4)*zeta(5)/63) * Product_{p prime} (1 - 2/p^5 + 1/p^9) = 0.01658573169... . (End)

Mathematica

f[p_, e_] := p^(4*e - 4)*(1 + p + p^2 + p^3 + p^4); a[1] = 63; a[n_] := 63 * Times @@ f @@@ FactorInteger[n]; Array[a, 25] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 63 * prod(i = 1, #f~, (f[i, 1]^4 + f[i, 1]^3 + f[i, 1]^2 + f[i, 1] + 1)*f[i, 1]^(4*f[i, 2] - 4)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013662, A013663, A160893.

Sequence in context: A243214 A341569 A005463 * A017779 A110826 A017726

Adjacent sequences: A160893 A160894 A160895 * A160897 A160898 A160899

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved