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 A379814 #9 Jan 03 2025 09:37:02
%S A379814 1,45,280,1533,3276,12600,17200,49725,68887,147420,162504,429240,
%T A379814 373660,774000,917280,1596221,1425060,3099915,2483320,5022108,4816000,
%U A379814 7312680,6449040,13923000,10253901,16814700,16760800,26367600,20536380,41277600,28659904,51117885
%N A379814 a(n) = sigma_2(n) * sigma_3(n).
%C A379814 See A379812 for more links and Ramanujan's general formula.
%D A379814 Srinivasa Ramanujan, Collected papers, edited by G. H. Hardy et al., Chelsea, 1962, chapter 17, pp. 133-135.
%H A379814 Amiram Eldar, <a href="/A379814/b379814.txt">Table of n, a(n) for n = 1..10000</a>
%H A379814 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 A379814 a(n) = A001157(n) * A001158(n).
%F A379814 Multiplicative with a(p^e) = (p^(2*e+2)-1) * (p^(3*e+3)-1) / ((p^2-1) * (p^3-1)).
%F A379814 Dirichlet g.f.: zeta(s) * zeta(s-2) * zeta(s-3) * zeta(s-5) / zeta(2*s-5).
%F A379814 Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(3) * zeta(4) * zeta(6) / zeta(7) = Pi^10 * zeta(3) / (85050 * zeta(7)) = 1.31261826893951336264... .
%t A379814 a[n_] := Times @@ DivisorSigma[{2, 3}, n]; Array[a, 50]
%o A379814 (PARI) a(n) = {my(f = factor(n)); sigma(f, 2) * sigma(f, 3);}
%Y A379814 Cf. A001157, A001158, A091260, A092344, A092344, A298754, A379812, A379813.
%Y A379814 Cf. A002117, A013662, A013664, A013665.
%K A379814 nonn,easy,mult
%O A379814 1,2
%A A379814 _Amiram Eldar_, Jan 03 2025