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 A083238 #24 May 10 2024 04:22:18
%S A083238 1,0,3,1,6,0,12,-4,19,-6,24,-12,40,-26,50,-26,57,-39,78,-58,100,-68,
%T A083238 104,-80,140,-109,151,-111,167,-137,209,-177,240,-192,246,-198,289,
%U A083238 -251,311,-255,345,-303,399,-355,439,-361,433,-385,509,-452,545,-473,571,-517,637,-565,685,-605,695,-635,803,-741,837,-733,860
%N A083238 First order recursion: a(0)=1; a(n) = sigma(1,n) - a(n-1).
%C A083238 Provide interesting decomposition: sigma(n)=u+w, where u and w consecutive terms of this sequence; this depends also on initial value.
%H A083238 Harvey P. Dale, <a href="/A083238/b083238.txt">Table of n, a(n) for n = 0..1000</a>
%F A083238 It follows that a(n)+a(n-1) = A000203(n).
%t A083238 f[x_] := DivisorSigma[1, x]-f[x-1] f[0]=1; Table[f[w], {w, 1, 100}]
%t A083238 nxt[{n_,a_}]:={n+1,DivisorSigma[1,n+1]-a}; NestList[nxt,{0,1},70][[;;,2]] (* _Harvey P. Dale_, May 10 2024 *)
%o A083238 (PARI) lista(nn) = {my(last = 1, v=vector(nn)); for (n=1, nn, v[n] = sigma(n) - last; last = v[n]; ); concat(1, v); } \\ _Michel Marcus_, Mar 28 2020
%Y A083238 Cf. A000203, A083236, A083237.
%K A083238 sign
%O A083238 0,3
%A A083238 _Labos Elemer_, Apr 23 2003