cp's OEIS Frontend

A361147 a(n) = sigma(n)^3.

%I A361147 #10 Mar 10 2023 12:14:23
%S A361147 1,27,64,343,216,1728,512,3375,2197,5832,1728,21952,2744,13824,13824,
%T A361147 29791,5832,59319,8000,74088,32768,46656,13824,216000,29791,74088,
%U A361147 64000,175616,27000,373248,32768,250047,110592,157464,110592,753571,54872,216000,175616
%N A361147 a(n) = sigma(n)^3.
%F A361147 Multiplicative with a(p^e) = ((p^(e+1)-1)/(p-1))^3.
%F A361147 Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(s-2) * zeta(s-3) * Product_{primes p} (1 + 1/p^(2*s-3) + 2/p^(s-1) + 2/p^(s-2)).
%F A361147 Sum_{k=1..n} a(k) ~ c * Pi^6 * zeta(3) * n^4 / 2160, where c = Product_{primes p} (1 + 2/p^2 + 2/p^3 + 1/p^5) = 2.83598357433419286770442457158038489640898183...
%F A361147 a(n) = A000578(A000203(n)).
%t A361147 Table[DivisorSigma[1, n]^3, {n, 1, 50}]
%o A361147 (PARI) a(n) = sigma(n)^3;
%o A361147 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + p*X*(2 + 2*p + p^2*X)) / ((1-X)*(1-p*X)*(1-p^2*X)*(1-p^3*X)))[n], ", "))
%Y A361147 Cf. A000203, A024916, A072861, A072379, A361179.
%Y A361147 Cf. A000005, A000578, A035116, A319089.
%K A361147 nonn,mult
%O A361147 1,2
%A A361147 _Vaclav Kotesovec_, Mar 02 2023