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 A344080 #14 May 11 2021 10:32:27
%S A344080 1,5,9,98,33,4225,129,72354,20196,1050625,2049,2194099186,8193,
%T A344080 268468225,1073807361,156925970179,131073,101629064089930,524289,
%U A344080 3657261440572306,4398050705409,17592194433025,8388609,4727105427440383342818,847322163876,4503599761588225
%N A344080 a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n.
%H A344080 Seiichi Manyama, <a href="/A344080/b344080.txt">Table of n, a(n) for n = 1..719</a>
%F A344080 G.f.: Sum_{k >= 1} (tau(k) * x)^k/(1 - (tau(k) * x)^k).
%F A344080 If p is prime, a(p) = 1 + 2^p.
%t A344080 a[n_] := DivisorSum[n, DivisorSigma[0, #]^n &]; Array[a, 26] (* _Amiram Eldar_, May 09 2021 *)
%o A344080 (PARI) a(n) = sumdiv(n, d, numdiv(d)^n);
%o A344080 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-(numdiv(k)*x)^k)))
%Y A344080 Cf. A007425, A062367, A097988, A279789, A344060, A344081.
%K A344080 nonn
%O A344080 1,2
%A A344080 _Seiichi Manyama_, May 09 2021