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 A386012 #17 Aug 03 2025 06:47:46
%S A386012 1,16,54,192,250,864,686,2048,2187,4000,2662,10368,4394,10976,13500,
%T A386012 20480,9826,34992,13718,48000,37044,42592,24334,110592,46875,70304,
%U A386012 78732,131712,48778,216000,59582,196608,143748,157216,171500,419904,101306,219488,237276,512000
%N A386012 a(n) = n^3*tau(n).
%C A386012 Dirichlet convolution of the cubes A000578 with themselves.
%H A386012 Amiram Eldar, <a href="/A386012/b386012.txt">Table of n, a(n) for n = 1..10000</a>
%F A386012 a(n) = n*A034714(n) = n^2*A038040(n).
%F A386012 Dirichlet g.f.: zeta^2(s-3).
%F A386012 From _Amiram Eldar_, Jul 15 2025 (Start)
%F A386012 Multiplicative with a(p^e) = p^(3*e) * (e+1).
%F A386012 Sum_{k=1..n} a(k) ~ (n^4/4) * (log(n) + 2*gamma - 1/4), where gamma is Euler's constant (A001620). (End)
%F A386012 G.f.: Sum_{k>=1} k^3*x^k*(1 + 4*x^k + x^(2*k)) / (1-x^k)^4. - _Vaclav Kotesovec_, Aug 03 2025
%p A386012 seq( n^3*numtheory[tau](n),n=1..100) ;
%t A386012 a[n_]:=n^3*DivisorSigma[0,n]; Array[a,40] (* _Stefano Spezia_, Jul 14 2025 *)
%t A386012 nmax = 40; Rest[CoefficientList[Series[Sum[k^3*x^k*(1 + 4*x^k + x^(2*k))/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 03 2025 *)
%o A386012 (PARI) a(n) = n^3 * numdiv(n); \\ _Amiram Eldar_, Jul 15 2025
%Y A386012 Cf. A000005, A001620, A034714, A038040, A320895 (partial sums), A372928 (Mobius transform).
%K A386012 nonn,mult,easy
%O A386012 1,2
%A A386012 _R. J. Mathar_, Jul 14 2025