A362136 - OEIS

%I #7 Apr 14 2023 11:35:42

%S 1,2,2,2,2,3,3,2,4,4,4,2,5,5,6,5,6,6,5,5,8,5,5,8,6,6,8,8,10,7,8,7,8,8,

%T 7,6,9,11,11,13,9,10,13,12,8,9,15,16,13,11,10,12,13,16,13,17,17,12,15,

%U 18,23,18,12,12,13,24,12,16,20,15,20,19,21,22,12,13,15,15,12,23,21,22,24,13,5,23

%N First differences of A362135.

%C Alternatively, row lengths of A360179 read as an irregular triangle of rows whose terms strictly increase.

%H Michael De Vlieger, <a href="/A362136/b362136.txt">Table of n, a(n) for n = 1..47545</a>

%H Michael De Vlieger, <a href="/A362136/a362136.png">Scatterplot of a(n)</a>, n = 1..47545.

%e A360179 read as an irregular triangle of subsequences whose terms are nondecreasing.

%e    n: row n of A360179    a(n)

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

%e    1: 1;                    1

%e    2: 1, 2;                 2

%e    3: 2, 3;                 2

%e    4: 2, 4;                 2

%e    5: 3, 5;                 2

%e    6: 2, 4,  6;             3

%e    7: 4, 6,  8;             3

%e    8: 4, 7;                 2

%e    9: 2, 5,  7, 10;         4

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

%e   11: 6, 8, 12, 16;         4

%e   12: 5, 9;                 2

%e   etc.

%t nn = 960;

%t c[_] := False; m = 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[n - 1 - m]; Set[m, n - 1] ];

%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. A360179, A362134, A362135.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Apr 10 2023