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%I #15 Sep 26 2020 09:15:38
%S 1,8,27,64,125,216,343,504,729,1000,1331,1728,2197,2744,3375,4032,
%T 4913,5832,6859,8000,9261,10648,12167,13608,15625,17576,19656,21952,
%U 24389,27000,29791,32256,35937,39304,42875,46656,50653,54872,59319
%N Coefficients of the Dirichlet series zeta(s-3) / zeta(3s-3).
%H Álvar Ibeas, <a href="/A254521/b254521.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n^3 * Sum_{d^3 | n} (moebius(d) / d^6).
%F Multiplicative with a(p) = p^3; a(p^2) = p^6; a(p^e) = p^(3e) - p^(3e-6), for e > 2.
%F Sum_{k=1..n} a(k) ~ n^4 / (4*Zeta(9)). - _Vaclav Kotesovec_, Feb 03 2019
%F Sum_{k>=1} 1/a(k) = Product_{p prime} (1 + 1/p^3 + 1/p^6 + 1/((p^3 - 1)^2*(p^3 + 1))) = 1.202094253239358480267688474077353358147971390519883358936462981705245... - _Vaclav Kotesovec_, Sep 26 2020
%o (PARI) a(n) = n^3*sumdiv(n, d, if (ispower(d, 3), moebius(sqrtnint(d, 3))/d^2)); \\ _Michel Marcus_, Feb 10 2015
%o (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - p^3*X)*(1 - p^3*X^3))[n], ", ")) \\ _Vaclav Kotesovec_, Sep 26 2020
%Y Cf. A000578.
%K mult,nonn
%O 1,2
%A _Álvar Ibeas_, Jan 31 2015