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 A065805 #32 Mar 02 2025 10:01:09
%S A065805 2,10,44,377,3912,57214,960808,19261862,435877584,11123320200,
%T A065805 313842837684,9729290348250,328114698808288,11967567841654610,
%U A065805 469172063576559648,19676848703371278527,878942778254232811956,41661071646298278566892,2088331858752553232964220
%N A065805 a(n) = Sum_{j=0..n} sigma_j(n).
%H A065805 Amiram Eldar, <a href="/A065805/b065805.txt">Table of n, a(n) for n = 1..386</a> (terms 1..100 from Harry J. Smith)
%F A065805 a(n) ~ n^(n+1) / (n-1). - _Vaclav Kotesovec_, Sep 11 2018
%F A065805 a(n) = n + 1 + Sum_{d|n, d<n} (d^(n+1) - 1)/(d - 1). - _Amiram Eldar_, Mar 02 2025
%e A065805 For n = 6, a(6) = 4 + 12 + 50 + 252 + 1394 + 8052 + 47450 = 57214.
%t A065805 a[n_] := Apply[Plus, Table[DivisorSigma[w, n], {w, 0, n}]]; Array[a, 30]
%t A065805 a[n_] := DivisorSum[n, (#^(n + 1) - 1)/(# - 1) &, # > 1 &] + n + 1; Array[a, 30] (* _Amiram Eldar_, Mar 01 2025 *)
%o A065805 (PARI) a(n) = sum(j=0, n, sigma(n, j)); \\ _Harry J. Smith_, Oct 31 2009
%o A065805 (PARI) a(n) = sumdiv(n, d, if(d == 1, n+1, (d^(n+1) - 1)/(d - 1))); \\ _Amiram Eldar_, Mar 01 2025
%Y A065805 Cf. A000005, A000203, A001157, A319194.
%K A065805 nonn
%O A065805 1,1
%A A065805 _Labos Elemer_, Nov 21 2001