%I #19 Dec 29 2022 11:22:59
%S 1,3,4,7,13,18,20,23,28,31,43,58,72,78,90,93,97,112,132,150,151,169,
%T 193,194,225,225,233,253,259,271,272,293,301,355,403,408,446,506,562,
%U 580,590,623,667,703,727,751,799,832,851,884,900,908,920,944,972,1008,1010,1028,1040
%N a(n) = Sum_{i=n-k..n} sigma(i) which is not less than a(n-1) and obtained with the least k.
%C Is this sequence well defined?
%e a(1) to a(4) are sigma(n) as these increase: 1 3 4 7. sigma(5)=6 and as this decreases, we examine sigma(5)+sigma(4)=7+6=13.
%o (PARI) lista(nn) = my(v=vector(nn)); v[1]=sigma(1); for (i=2, nn, k=0; while (sum(j=i-k, i, sigma(j))<v[i-1], k++); v[i]=sum(j=i-k, i, sigma(j))); v; \\ edited by _Michel Marcus_, Dec 28 2022
%Y Cf. A000203, A093125.
%K nonn
%O 1,2
%A _Jon Perry_, Mar 22 2004
%E Name edited by and more terms from _Michel Marcus_, Dec 28 2022