[go: up one dir, main page]

login
A083238
First order recursion: a(0)=1; a(n) = sigma(1,n) - a(n-1).
3
1, 0, 3, 1, 6, 0, 12, -4, 19, -6, 24, -12, 40, -26, 50, -26, 57, -39, 78, -58, 100, -68, 104, -80, 140, -109, 151, -111, 167, -137, 209, -177, 240, -192, 246, -198, 289, -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
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
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