This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319089 #26 Feb 16 2025 08:33:56
%S A319089 1,8,8,27,8,64,8,64,27,64,8,216,8,64,64,125,8,216,8,216,64,64,8,512,
%T A319089 27,64,64,216,8,512,8,216,64,64,64,729,8,64,64,512,8,512,8,216,216,64,
%U A319089 8,1000,27,216,64,216,8,512,64,512,64,64,8,1728,8,64,216,343
%N A319089 a(n) = tau(n)^3, where tau is A000005.
%H A319089 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.
%F A319089 Multiplicative with a(p^e) = (e+1)^3. - _Amiram Eldar_, Dec 31 2022
%F A319089 a(n) = Sum_{d1|n} Sum_{d2|n} tau(d1*d2). - _Ridouane Oudra_, Mar 07 2023
%F A319089 From _Vaclav Kotesovec_, Mar 09 2023: (Start)
%F A319089 Dirichlet g.f.: Product_{p prime} p^(2*s) * (1 + 4*p^s + p^(2*s)) / (p^s - 1)^4.
%F A319089 Dirichlet g.f.: zeta(s)^8 * Product_{p prime} (1 - 9/p^(2*s) + 16/p^(3*s) - 9/p^(4*s) + 1/p^(6*s)), (with a product that converges for s=1). (End)
%p A319089 with(numtheory): seq(tau(n)^3, n=1..100); # _Ridouane Oudra_, Mar 07 2023
%t A319089 DivisorSigma[0, Range[100]]^3
%o A319089 (PARI) a(n) = numdiv(n)^3; \\ _Altug Alkan_, Sep 10 2018
%o A319089 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 4*X + X^2)/(1 - X)^4)[n], ", ")) \\ _Vaclav Kotesovec_, Mar 09 2023
%Y A319089 Cf. A000005, A006218, A035116, A061502, A318755 (partial sums).
%K A319089 nonn,easy,mult
%O A319089 1,2
%A A319089 _Vaclav Kotesovec_, Sep 10 2018