%I #12 Apr 14 2023 11:36:16
%S 1,2,3,4,5,6,8,10,12,16,19,22,28,32,34,40,43,47,51,53,56,57,60,63,64,
%T 65,69,75,77,79,80,84,86,98,99,102,105,107,119,129,130,141,143,146,
%U 150,162,170,182,188,200,202,214,220,226,232,240,248,252,262,264,268,282,294,310,326,330,342,354,362
%N Records in A360179.
%H Michael De Vlieger, <a href="/A362127/b362127.txt">Table of n, a(n) for n = 1..8238</a>
%H Michael De Vlieger, <a href="/A362127/a362127.png">Labeled scatterplot of m = A360179(n)</a> for n = 1..512. Records, terms of this sequence, appear in red, local minima in blue, terms following novel m in gold and by extant m in green. The cyan line indicates the smallest number u not in a(1..n) and is not a feature of the sequence itself. The magenta line indicates the "prevailing low" L(n) and is not a feature of the sequence itself.
%t nn = 10^4; c[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];
%t a[1] = j = u = 1; r = 0;
%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], j}, {k, k}]; While[h[u] == 0, u++];
%t If[k > r, r = k; Sow[r]], {n, 2, nn}] ][[-1, -1]]
%Y Cf. A000005, A360179, A362128.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Apr 09 2023