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 A027847 #49 Aug 27 2023 02:54:47
%S A027847 1,11,31,95,131,341,351,775,850,1441,1343,2945,2211,3861,4061,6231,
%T A027847 4931,9350,6879,12445,10881,14773,12191,24025,16406,24321,22990,33345,
%U A027847 24419,44671,29823,49911,41633,54241,45981,80750,50691,75669,68541,101525,68963,119691,79551,127585,111350
%N A027847 a(n) = Sum_{d|n} sigma(n/d)*d^3.
%H A027847 Seiichi Manyama, <a href="/A027847/b027847.txt">Table of n, a(n) for n = 1..1000</a>
%F A027847 Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(s-3). - Corrected by _Álvar Ibeas_, Jan 31 2015
%F A027847 Multiplicative with a(p^e) = (p^(3e+5) - (p^2+p+1)*p^(e+1) + p + 1) / ((p^3-1)*(p^2-1)). - _Mitch Harris_, Jun 27 2005
%F A027847 L.g.f.: -log(Product_{k>=1} (1 - x^k)^sigma_2(k)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 23 2018
%F A027847 Sum_{k=1..n} a(k) ~ Pi^4 * zeta(3) * n^4 / 360. - _Vaclav Kotesovec_, Jan 31 2019
%t A027847 a[n_] := DivisorSum[n, DivisorSigma[1, n/#]*#^3&]; Array[a, 45] (* _Jean-François Alcover_, Dec 07 2015 *)
%t A027847 f[p_, e_] := (p^(3 e + 5) - (p^2 + p + 1)*p^(e + 1) + p + 1)/((p^3 - 1)*(p^2 - 1)); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* _Amiram Eldar_, Aug 27 2023 *)
%o A027847 (PARI) N=66; x='x+O('x^N);
%o A027847 c=sum(j=1,N,j*x^j);
%o A027847 t=log(1/prod(j=1,N, eta(x^(j))^(j^2)));
%o A027847 Vec(serconvol(t,c)) \\ _Joerg Arndt_, May 03 2008
%o A027847 (PARI) a(n) = sumdiv(n, d, sigma(n/d)*d^3); \\ _Michel Marcus_, Feb 24 2015
%Y A027847 Cf. A001001 (Dirichlet convolution of sigma and n^2), A275585.
%K A027847 nonn,mult,easy
%O A027847 1,2
%A A027847 _N. J. A. Sloane_