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.
{a(n)=polcoeff(exp(sum(m=1,n,x^m/m*sumdiv(m,d,d^sigma(d)))+x*O(x^n)),n)}
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.
a[n_] := DivisorSum[n, #^DivisorSigma[0, #] &]; Array[a, 30] (* Amiram Eldar, Oct 08 2021 *)
{a(n)=sumdiv(n,d,d^sigma(d,0))}
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
a(4) = Sum_{d|4} 4^sigma(d) = 4^1 + 4^3 + 4^7 = 16452.
a[n_] := DivisorSum[n, n^DivisorSigma[1, #] &]; Array[a, 16] (* Amiram Eldar, Jun 29 2021 *)
a(n) = sumdiv(n, d, n^sigma(d)); \\ Michel Marcus, Jun 29 2021
a[n_] := DivisorSum[n, #^(DivisorSigma[1, #] - 1) &]; Array[a, 14] (* Amiram Eldar, Oct 14 2021 *)
a(n) = sumdiv(n, d, d^(sigma(d)-1));
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(sigma(k)-1)*x^k/(1-x^k)))
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