A092406 a(1)=1, a(n) = sigma(n) if sigma(n) >= a(n-1), otherwise a(n) = a(n-1) + sigma(n).

1, 3, 4, 7, 13, 25, 33, 48, 61, 79, 91, 119, 133, 157, 181, 212, 230, 269, 289, 331, 363, 399, 423, 483, 514, 556, 596, 652, 682, 754, 786, 849, 897, 951, 999, 1090, 1128, 1188, 1244, 1334, 1376, 1472, 1516, 1600, 1678, 1750, 1798, 1922, 1979, 2072, 2144, 2242

Offset

1,2

Comments

Does a(n)=sigma(n) only for n=1,2,3,4?

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A024916(n) - 8 and A160664(n) - 9, for n > 3. - Greg Dresden, Feb 23 2020

Mathematica

nxt[{n_, a_}]:=Module[{s=DivisorSigma[1, n+1]}, {n+1, If[s>=a, s, a+s]}]; NestList[ nxt, {1, 1}, 60][[All, 2]] (* Harvey P. Dale, Aug 04 2022 *)

Prog

(PARI) { v=vector(60); v[1]=sigma(1); for (i=2, 60, if (sigma(i)<v[i-1], v[i]=v[i-1]+sigma(i), v[i]=sigma(i))); v }
(Python)
from math import isqrt
def A092406(n): return (-(s:=isqrt(n))**2*(s+1) + sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1))>>1)-8 if n>3 else (1 if n<2 else n+1) # Chai Wah Wu, Oct 22 2023

Crossrefs

Cf. A000203, A024916, A160664.

Sequence in context: A116201 A280224 A282718 * A250297 A254310 A121174

Adjacent sequences: A092403 A092404 A092405 * A092407 A092408 A092409

Keyword

nonn

Author

Jon Perry, Mar 22 2004

Status

approved