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

%I A092406 #17 Oct 22 2023 16:35:57
%S A092406 1,3,4,7,13,25,33,48,61,79,91,119,133,157,181,212,230,269,289,331,363,
%T A092406 399,423,483,514,556,596,652,682,754,786,849,897,951,999,1090,1128,
%U A092406 1188,1244,1334,1376,1472,1516,1600,1678,1750,1798,1922,1979,2072,2144,2242
%N A092406 a(1)=1, a(n) = sigma(n) if sigma(n) >= a(n-1), otherwise a(n) = a(n-1) + sigma(n).
%C A092406 Does a(n)=sigma(n) only for n=1,2,3,4?
%H A092406 Harvey P. Dale, <a href="/A092406/b092406.txt">Table of n, a(n) for n = 1..1000</a>
%F A092406 a(n) = A024916(n) - 8 and A160664(n) - 9, for n > 3. - _Greg Dresden_, Feb 23 2020
%t A092406 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 *)
%o A092406 (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 }
%o A092406 (Python)
%o A092406 from math import isqrt
%o A092406 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
%Y A092406 Cf. A000203, A024916, A160664.
%K A092406 nonn
%O A092406 1,2
%A A092406 _Jon Perry_, Mar 22 2004