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 A174937 #16 Oct 14 2021 08:43:21
%S A174937 1,5,10,69,26,1310,50,4165,739,10030,122,2987358,170,38470,50660,
%T A174937 1052741,290,34014263,362,64010094,194540,234382,530,110078305630,
%U A174937 15651,457150,532180,481928838,842,656100061960
%N A174937 a(n) = Sum_{d|n} d^tau(d).
%C A174937 Here tau(n) = A000005(n) = the number of divisors of n.
%H A174937 Seiichi Manyama, <a href="/A174937/b174937.txt">Table of n, a(n) for n = 1..10000</a>
%F A174937 Also a(n) = Sum_{d|n} A007955(d)^2, where A007955(m) = product of divisors of m.
%F A174937 Logarithmic derivative of A174473.
%F A174937 G.f.: Sum_{k>=1} k^tau(k) * x^k/(1 - x^k). - _Seiichi Manyama_, Oct 14 2021
%e A174937 For n = 4, A007955(n) = b(n): a(4) = b(1)^2 + b(2)^2 + b(4)^2 = 1^2 + 2^2 + 8^2 = 69.
%t A174937 a[n_] := DivisorSum[n, #^DivisorSigma[0, #] &]; Array[a, 30] (* _Amiram Eldar_, Oct 08 2021 *)
%o A174937 (PARI) {a(n)=sumdiv(n,d,d^sigma(d,0))}
%o A174937 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k^numdiv(k)*x^k/(1-x^k))) \\ _Seiichi Manyama_, Oct 14 2021
%Y A174937 Cf. A000005 (tau), A174472, A174473, A345270, A345271.
%K A174937 nonn
%O A174937 1,2
%A A174937 _Jaroslav Krizek_ and _Paul D. Hanna_, Apr 02 2010