%I #9 Apr 14 2023 11:35:58
%S 2,3,4,5,6,7,9,11,13,14,17,20,21,23,29,35,37,38,44,46,50,94,100,120,
%T 121,124,125,136,139,140,142,144,148,178,185,186,187,189,193,195,197,
%U 201,203,209
%N Records in A362131.
%C No more records in A362131(n) for n <= 2^28.
%H Michael De Vlieger, <a href="/A362132/a362132.png">Plot (log_2 A362133(n), a(n)) at (x, y)</a>.
%t nn = 2^20;
%t c[_] := False; q[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];
%t a[1] = j = u = w = 1;
%t Reap[Do[
%t If[c[j],
%t k = j + f[u]; h[j]++; h[u]--,
%t k = f[j]; c[j] = True; h[j]++ ];
%t u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
%t While[h[u] == 0, u++];
%t If[k == w, While[q[w], w++]; Sow[w]], {n, 2, nn}] ][[-1, -1]]
%Y Cf. A360179, A362131, A362133.
%K nonn,more
%O 1,1
%A _Michael De Vlieger_, Apr 10 2023