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 A360823 #15 Jul 31 2023 02:25:11
%S A360823 1,4,6,20,10,96,14,256,288,650,22,4200,26,4004,11160,18784,34,70758,
%T A360823 38,164140,196098,136664,46,1756728,393800,747890,3287844,5452076,58,
%U A360823 22563060,62,31220032,50767926,20059286,41640130,391194396,74,99622016,725647728,1298396440
%N A360823 Expansion of Sum_{k>0} k * x^k / (1 - k * x^k)^(k+1).
%F A360823 a(n) = Sum_{d|n} d^(n/d) * binomial(d+n/d-1,d).
%F A360823 If p is prime, a(p) = 2 * p.
%t A360823 a[n_] := DivisorSum[n, #^(n/#) * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* _Amiram Eldar_, Jul 31 2023 *)
%o A360823 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^(k+1)))
%o A360823 (PARI) a(n) = sumdiv(n, d, d^(n/d)*binomial(d+n/d-1, d));
%Y A360823 Cf. A338658, A360794, A360824.
%K A360823 nonn
%O A360823 1,2
%A A360823 _Seiichi Manyama_, Feb 22 2023