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 A321598 #22 Jan 02 2025 09:36:03
%S A321598 1,9,31,89,176,375,589,1049,1516,2384,3147,4823,5916,8437,10406,14105,
%T A321598 16474,22380,25271,33264,37810,47683,52901,68183,73301,91100,100174,
%U A321598 122197,130356,161750,169137,205593,219162,259242,272714,330524,338144,400719,421686,493424
%N A321598 a(n) = Sum_{d|n} d*binomial(d+2,3).
%C A321598 Inverse Möbius transform of A002417.
%H A321598 Amiram Eldar, <a href="/A321598/b321598.txt">Table of n, a(n) for n = 1..10000</a>
%H A321598 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F A321598 G.f.: Sum_{k>=1} x^k*(1 + 3*x^k)/(1 - x^k)^5.
%F A321598 G.f.: Sum_{k>=1} k*A000292(k)*x^k/(1 - x^k).
%F A321598 L.g.f.: -log(Product_{k>=1} (1 - x^k)^A000292(k)) = Sum_{n>=1} a(n)*x^n/n.
%F A321598 Dirichlet g.f.: (zeta(s-4) + 3*zeta(s-3) + 2*zeta(s-2))*zeta(s)/6.
%F A321598 a(n) = (2*sigma_2(n) + 3*sigma_3(n) + sigma_4(n))/6.
%F A321598 a(n) = Sum_{d|n} A002417(d).
%F A321598 Sum_{k=1..n} a(k) ~ zeta(5) * n^5 / 30. - _Vaclav Kotesovec_, Feb 02 2019
%t A321598 Table[Sum[d Binomial[d + 2, 3], {d, Divisors[n]}], {n, 40}]
%t A321598 nmax = 40; Rest[CoefficientList[Series[Sum[x^k (1 + 3 x^k)/(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x]]
%t A321598 Table[(2 DivisorSigma[2, n] + 3 DivisorSigma[3, n] + DivisorSigma[4, n])/6, {n, 40}]
%o A321598 (PARI) a(n) = my(f = factor(n)); (sigma(f, 4) + 3*sigma(f, 3) + 2*sigma(f, 2)) / 6; \\ _Amiram Eldar_, Jan 02 2025
%Y A321598 Cf. A000292, A000335, A001157, A001158, A001159, A002417, A013663, A059358, A278403.
%K A321598 nonn,easy
%O A321598 1,2
%A A321598 _Ilya Gutkovskiy_, Nov 14 2018