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A362134 Novel terms in A360179, in order of appearance.

%I A362134 #14 Mar 26 2025 08:32:17
%S A362134 1,2,3,4,5,6,8,7,10,12,16,9,11,13,15,19,14,18,22,17,20,28,24,32,26,21,
%T A362134 31,25,34,27,33,23,30,40,36,29,35,39,37,43,42,47,51,45,41,38,49,44,53,
%U A362134 48,52,56,57,60,55,59,63,64,61,65,69,67,54,66,58,75,77,71,72,70,79,73,62,78,68,76,80,84
%N A362134 Novel terms in A360179, in order of appearance.
%C A362134 In other words, numbers A360179(n) that do not appear in A360179(1..n-1).
%C A362134 Row maxima of A360179, read as an irregular triangle of rows whose terms strictly increase.
%H A362134 Michael De Vlieger, <a href="/A362134/b362134.txt">Table of n, a(n) for n = 1..58188</a>
%H A362134 Michael De Vlieger, <a href="/A362134/a362134.png">Scatterplot of a(n)</a> n = 1..47545 (all novel terms that appear in A360179(1..2^28)).
%F A362134 A362127 contains records in this sequence.
%e A362134 A360179 read as an irregular triangle with rows of length A362135(n):
%e A362134    n: row n
%e A362134   --------------
%e A362134    1: 1;
%e A362134    2: 1, 2;
%e A362134    3: 2, 3;
%e A362134    4: 2, 4;
%e A362134    5: 3, 5;
%e A362134    6: 2, 4,  6;
%e A362134    7: 4, 6,  8;
%e A362134    8: 4, 7;
%e A362134    9: 2, 5,  7, 10;
%e A362134   10: 4, 7, 10, 12;
%e A362134   11: 6, 8, 12, 16;
%e A362134   12: 5, 9;
%e A362134   etc.
%e A362134 Terms in this sequence appear at the end of the rows as consequence of the definition of A360179.
%t A362134 nn = 800;
%t A362134 c[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];
%t A362134 a[1] = j = u = w = 1;
%t A362134 {1}~Join~Rest@ Reap[Do[
%t A362134       If[c[j],
%t A362134         k = j + f[u]; h[j]++; h[u]--,
%t A362134         k = f[j]; c[j] = True; h[j]++; Sow[j] ];
%t A362134       u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
%t A362134       While[h[u] == 0, u++], {n, 2, nn}] ][[-1, -1]]
%Y A362134 Cf. A000005, A360179, A362127, A362135.
%K A362134 nonn
%O A362134 1,2
%A A362134 _Michael De Vlieger_, Apr 10 2023