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A330725 a(0) = 0; thereafter a(n) = a(n-1) + sigma(n) if sigma(n) > a(n-1), otherwise a(n) = a(n-1) - sigma(n), where sigma is the sum of divisors function A000203.

%I A330725 #29 May 14 2022 19:05:52
%S A330725 0,1,4,0,7,1,13,5,20,7,25,13,41,27,3,27,58,40,1,21,63,31,67,43,103,72,
%T A330725 30,70,14,44,116,84,21,69,15,63,154,116,56,0,90,48,144,100,16,94,22,
%U A330725 70,194,137,44,116,18,72,192,120,0,80,170,110,278,216,120,16
%N A330725 a(0) = 0; thereafter a(n) = a(n-1) + sigma(n) if sigma(n) > a(n-1), otherwise a(n) = a(n-1) - sigma(n), where sigma is the sum of divisors function A000203.
%H A330725 Alois P. Heinz, <a href="/A330725/b330725.txt">Table of n, a(n) for n = 0..20000</a>
%p A330725 a:= proc(n) option remember; `if`(n=0, 0, ((s, t)-> s+
%p A330725       `if`(s<t, t, -t))(a(n-1), numtheory[sigma](n)))
%p A330725     end:
%p A330725 seq(a(n), n=0..80);
%t A330725 nxt[{n_,a_}]:={n+1,If[DivisorSigma[1,n+1]>a,a+DivisorSigma[1,n+1],a- DivisorSigma[ 1,n+1]]}; NestList[nxt,{0,0},70][[All,2]] (* _Harvey P. Dale_, May 14 2022 *)
%Y A330725 Cf. A000203, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A331165.
%K A330725 nonn,look
%O A330725 0,3
%A A330725 _Alois P. Heinz_, Jan 11 2020