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A362127 Records in A360179.

%I A362127 #12 Apr 14 2023 11:36:16
%S A362127 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 A362127 65,69,75,77,79,80,84,86,98,99,102,105,107,119,129,130,141,143,146,
%U A362127 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 A362127 Records in A360179.
%H A362127 Michael De Vlieger, <a href="/A362127/b362127.txt">Table of n, a(n) for n = 1..8238</a>
%H A362127 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 A362127 nn = 10^4; c[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];
%t A362127 a[1] = j = u = 1; r = 0;
%t A362127 Reap[Do[
%t A362127     If[c[j],
%t A362127       k = j + f[u]; h[j]++; h[u]--,
%t A362127       k = f[j]; c[j] = True; h[j]++ ];
%t A362127     u = Min[u, j]; Set[{a[n], j}, {k, k}]; While[h[u] == 0, u++];
%t A362127     If[k > r, r = k; Sow[r]], {n, 2, nn}] ][[-1, -1]]
%Y A362127 Cf. A000005, A360179, A362128.
%K A362127 nonn
%O A362127 1,2
%A A362127 _Michael De Vlieger_, Apr 09 2023