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 A333844 #18 Jan 24 2024 12:19:06
%S A333844 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,
%T A333844 1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,
%U A333844 1,1,1,1,1,1,1,1,1,1,1,3,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3
%N A333844 G.f.: Sum_{k>=1} k * x^(k^4) / (1 - x^(k^4)).
%C A333844 Sum of 4th roots of 4th powers dividing n.
%H A333844 Amiram Eldar, <a href="/A333844/b333844.txt">Table of n, a(n) for n = 1..10000</a>
%H A333844 A. Dixit, B. Maji, and A. Vatwani, <a href="https://arxiv.org/abs/2303.09937">Voronoi summation formula for the generalized divisor function sigma_z^k(n)</a>, arXiv:2303.09937 [math.NT], 2023, sigma(z=1,k=4,n).
%F A333844 Dirichlet g.f.: zeta(s) * zeta(4*s-1).
%F A333844 If n = Product (p_j^k_j) then a(n) = Product ((p_j^(floor(k_j/4) + 1) - 1)/(p_j - 1)).
%F A333844 Sum_{k=1..n} a(k) ~ zeta(3)*n + zeta(1/2)*sqrt(n)/2. - _Vaclav Kotesovec_, Dec 01 2020
%t A333844 nmax = 112; CoefficientList[Series[Sum[k x^(k^4)/(1 - x^(k^4)), {k, 1, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x] // Rest
%t A333844 Table[DivisorSum[n, #^(1/4) &, IntegerQ[#^(1/4)] &], {n, 112}]
%t A333844 f[p_, e_] := (p^(Floor[e/4] + 1) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Dec 01 2020 *)
%Y A333844 Cf. A000203, A053164, A063775, A069290, A300909, A333843.
%K A333844 nonn,mult
%O A333844 1,16
%A A333844 _Ilya Gutkovskiy_, Apr 07 2020