A160956 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 9.

511, 130305, 1676080, 16679040, 49902216, 427400400, 490968800, 2134917120, 3665586960, 12725065080, 10953738768, 54707251200, 34736533160, 125197044000, 163679268480, 273269391360, 222788253240, 934724674800, 482144484080, 1628808330240, 1610377664000

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from G. C. Greubel)

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) = 511*A160908(n). - R. J. Mathar, Mar 16 2016

From Amiram Eldar, Nov 08 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^8, where c = (511/8) * Product_{p prime} (1 + (p^7-1)/((p-1)*p^8)) = 123.8157549... .

Sum_{k>=1} 1/a(k) = (zeta(7)*zeta(8)/511) * Product_{p prime} (1 - 2/p^8 + 1/p^15) = 0.001965303453... . (End)

Mathematica

A160956[n_] := DivisorSum[n, MoebiusMu[n/#]*#^(9 - 1)/EulerPhi[n] &]; Table[511*A160956[n], {n, 1, 50}] (* G. C. Greubel, Dec 12 2017 *)
f[p_, e_] := p^(7*e - 7) * (p^8-1) / (p-1); a[1] = 511; a[n_] := 511 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)

Prog

(PARI) a(n) = {my(f = factor(n)); 511 * prod(i = 1, #f~, (f[i, 1]^8 - 1)*f[i, 1]^(7*f[i, 2] - 7)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022

Crossrefs

Cf. A000010, A013665, A013666, A160908.

Sequence in context: A258810 A321554 A321548 * A022191 A069384 A069410

Adjacent sequences: A160953 A160954 A160955 * A160957 A160958 A160959

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2009

Status

approved