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%I #19 Mar 28 2020 15:02:19
%S 1,0,3,1,6,0,12,-4,19,-6,24,-12,40,-26,50,-26,57,-39,78,-58,100,-68,
%T 104,-80,140,-109,151,-111,167,-137,209,-177,240,-192,246,-198,289,
%U -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 First order recursion: a(0)=1; a(n) = sigma(1,n) - a(n-1).
%C Provide interesting decomposition: sigma(n)=u+w, where u and w consecutive terms of this sequence; this depends also on initial value.
%F It follows that a(n)+a(n-1) = A000203(n).
%t f[x_] := DivisorSigma[1, x]-f[x-1] f[0]=1; Table[f[w], {w, 1, 100}]
%o (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 Cf. A000203, A083236, A083237.
%K sign
%O 0,3
%A _Labos Elemer_, Apr 23 2003
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