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 A379813 #9 Jan 03 2025 09:36:55
%S A379813 1,27,112,511,756,3024,2752,8775,9841,20412,15984,57232,30772,74304,
%T A379813 84672,145111,88452,265707,137200,386316,308224,431568,292032,982800,
%U A379813 488281,830844,817600,1406272,731700,2286144,953344,2359287,1790208,2388204,2080512,5028751
%N A379813 a(n) = sigma_1(n) * sigma_3(n).
%C A379813 See A379812 for more links and Ramanujan's general formula.
%D A379813 Srinivasa Ramanujan, Collected papers, edited by G. H. Hardy et al., Chelsea, 1962, chapter 17, pp. 133-135.
%H A379813 Amiram Eldar, <a href="/A379813/b379813.txt">Table of n, a(n) for n = 1..10000</a>
%H A379813 Srinivasa Ramanujan, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram17.html">Some formulae in the analytic theory of numbers</a>, Messenger of Mathematics, Vol. 45 (1916), pp. 81-84.
%F A379813 a(n) = A000203(n) * A001158(n).
%F A379813 Multiplicative with a(p^e) = (p^(e+1)-1) * (p^(3*e+3)-1) / ((p-1) * (p^3-1)).
%F A379813 Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(s-3) * zeta(s-4) / zeta(2*s-4).
%F A379813 Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = 7 * zeta(5) / 4 = 1.81462357150089737107... .
%t A379813 a[n_] := Times @@ DivisorSigma[{1, 3}, n]; Array[a, 50]
%o A379813 (PARI) a(n) = {my(f = factor(n)); sigma(f) * sigma(f, 3);}
%Y A379813 Cf. A000203, A001158, A013663, A072861, A091258, A091259, A092348, A092345, A356533, A356534, A379812, A379814.
%K A379813 nonn,easy,mult
%O A379813 1,2
%A A379813 _Amiram Eldar_, Jan 03 2025