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

Author

Jon Perry, Mar 22 2004

Keywords

• nonn

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

Crossrefs

Cf. A000203, A024916, A160664.

Programs

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 *)

PARI

{ v=vector(60); v[1]=sigma(1); for (i=2,60, if (sigma(i)
				

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

Formula

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