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%I #19 Oct 28 2022 07:14:40
%S 1,39,511,2359,12621,19929,101179,149943,368089,492219,1611831,
%T 1205449,4457701,3945981,6449331,9588151,22722609,14355471,44576623,
%U 29772939,51702469,62861409,141611691,76620873,196890121,173850339,268218727,238681261,574336533,251523909
%N a(n) = sigma_3(n^3)/sigma(n^3).
%H Amiram Eldar, <a href="/A077454/b077454.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001158(n^3)/A000203(n^3).
%F Multiplicative with a(p^e) = (p^(6*e+2) + p^(3*e+1) + 1)/(p^2 + p + 1). - _Amiram Eldar_, Sep 09 2020
%F Sum_{k=1..n} a(k) ~ c * n^7, where c = (zeta(7)*Pi^4/630) * Product_{p prime} (1 - 1/p^2 - 1/p^6 + 1/p^7 - 1/p^8 + 1/p^9) = 0.09343400455... . - _Amiram Eldar_, Oct 28 2022
%e a(2) = sigma_3(2^3)/sigma(2^3) = 585/15 = 39.
%t f[p_, e_] := (p^(6*e+2) + p^(3*e+1) + 1)/(p^2 + p + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 30] (* _Amiram Eldar_, Sep 09 2020 *)
%o (PARI) a(n)=sumdiv(n^3,d,d^3)/sigma(n^3)
%o (PARI) a(n) = my(f=factor(n^3)); sigma(f, 3)/sigma(f); \\ _Michel Marcus_, Sep 09 2020
%Y Cf. A000203, A000578, A001158, A013665, A057660, A077455, A077456.
%K nonn,easy,mult
%O 1,2
%A _Benoit Cloitre_, Nov 30 2002
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