A160894 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 5.

31, 465, 1240, 3720, 4836, 18600, 12400, 29760, 33480, 72540, 45384, 148800, 73780, 186000, 193440, 238080, 161820, 502200, 224440, 580320, 496000, 680760, 394320, 1190400, 604500, 1106700, 903960, 1488000, 783060, 2901600, 954304, 1904640, 1815360, 2427300

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) = 31*A160891(n). - R. J. Mathar, Mar 16 2016

From Amiram Eldar, Nov 08 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^4, where c = (31/4) * Product_{p prime} (1 + 1/p^2 + 1/p^3 + 1/p^4) = 14.3522727306... .

Sum_{k>=1} 1/a(k) = (zeta(3)*zeta(4)/31) * Product_{p prime} (1 - 2/p^4 + 1/p^7) = 0.03599754726... . (End)

Mathematica

f[p_, e_] := p^(3 e - 3)*(1 + p + p^2 + p^3); a[1] = 31; a[n_] := 31 * Times @@ f @@@ FactorInteger[n]; Array[a, 32] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 31 * prod(i = 1, #f~, (f[i, 1]^3 + f[i, 1]^2 + f[i, 1] + 1)*f[i, 1]^(3*f[i, 2] - 3)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A002117, A013662, A160891.

Sequence in context: A160443 A125466 A142280 * A010947 A022626 A042866

Adjacent sequences: A160891 A160892 A160893 * A160895 A160896 A160897

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved