%I
%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(n1).
%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(n1) = A000203(n).
%t f[x_] := DivisorSigma[1, x]f[x1] 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
