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,0)))+x*O(x^n)),n)}
a[n_] := DivisorSum[n, #^DivisorSigma[1, #] &]; Array[a, 16] (* Amiram Eldar, Oct 08 2021 *)
{a(n)=sumdiv(n,d,d^sigma(d))}
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^sigma(k)*x^k/(1-x^k))) \\ Seiichi Manyama, Oct 14 2021
a(10) = Sum_{d|10} d^tau(10/d) = 1^4 + 2^2 + 5^2 + 10^1 = 40.
Table[Sum[k^DivisorSigma[0, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]
a(n) = sumdiv(n, d, d^numdiv(n/d)); \\ Michel Marcus, Oct 08 2021
a(10) = Sum_{d|10} 10^tau(d) = 10^1 + 10^2 + 10^2 + 10^4 = 10210.
Table[Sum[n^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
a(n) = sumdiv(n, d, n^numdiv(d)); \\ Michel Marcus, Oct 08 2021
a[n_] := DivisorSum[n, #^(DivisorSigma[0, #] - 1) &]; Array[a, 40] (* Amiram Eldar, Oct 14 2021 *)
a(n) = sumdiv(n, d, d^(numdiv(d)-1));
my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k^(numdiv(k)-1)*x^k/(1-x^k)))
a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98.
Table[Sum[(n - k)^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
a(10) = Sum_{d|10} (10-d)^tau(10/d) = 9^4 + 8^2 + 5^2 + 0^1 = 6650.
Table[Sum[(n - k)^DivisorSigma[0, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
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