OFFSET
0,3
COMMENTS
Provide interesting decomposition: sigma(n)=u+w, where u and w consecutive terms of this sequence; this depends also on initial value.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
It follows that a(n)+a(n-1) = A000203(n).
MATHEMATICA
f[x_] := DivisorSigma[1, x]-f[x-1] f[0]=1; Table[f[w], {w, 1, 100}]
nxt[{n_, a_}]:={n+1, DivisorSigma[1, n+1]-a}; NestList[nxt, {0, 1}, 70][[;; , 2]] (* Harvey P. Dale, May 10 2024 *)
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Labos Elemer, Apr 23 2003
STATUS
approved