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URL: https://oeis.org/A160956

⇱ A160956 - OEIS

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A160956
a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 9.
1
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 19 2009
STATUS
approved