A362134 - OEIS

%I #10 Apr 14 2023 11:35:50

%S 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 31,25,34,27,33,23,30,40,36,29,35,39,37,43,42,47,51,45,41,38,49,44,53,

%U 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 Novel terms in A360179, in order of appearance.

%C In other words, numbers A360179(n) that do not appear in A360179(1..n-1).

%C Row maxima of A360179, read as an irregular triangle of rows whose terms strictly increase.

%H Michael De Vlieger, <a href="/A362134/b362134.txt">Table of n, a(n) for n = 1..58188</a>

%H 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 A362127 contains records in this sequence.

%e A360179 read as an irregular triangle with rows of length A362135(n):

%e    n: row n

%e   --------------

%e    1: 1;

%e    2: 1, 2;

%e    3: 2, 3;

%e    4: 2, 4;

%e    5: 3, 5;

%e    6: 2, 4,  6;

%e    7: 4, 6,  8;

%e    8: 4, 7;

%e    9: 2, 5,  7, 10;

%e   10: 4, 7, 10, 12;

%e   11: 6, 8, 12, 16;

%e   12: 5, 9;

%e   etc.

%e Terms in this sequence appear at the end of the rows as consequence of the definition of A360179.

%t nn = 800;

%t c[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];

%t a[1] = j = u = w = 1;

%t {1}~Join~Rest@ Reap[Do[

%t       If[c[j],

%t         k = j + f[u]; h[j]++; h[u]--,

%t         k = f[j]; c[j] = True; h[j]++; Sow[j] ];

%t       u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];

%t       While[h[u] == 0, u++], {n, 2, nn}] ][[-1, -1]]

%Y Cf. A000005, A360179, A362127, A362135.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Apr 10 2023