cp's OEIS Frontend

A362136 First differences of A362135.

%I A362136 #7 Apr 14 2023 11:35:42
%S A362136 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 A362136 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 A362136 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 A362136 First differences of A362135.
%C A362136 Alternatively, row lengths of A360179 read as an irregular triangle of rows whose terms strictly increase.
%H A362136 Michael De Vlieger, <a href="/A362136/b362136.txt">Table of n, a(n) for n = 1..47545</a>
%H A362136 Michael De Vlieger, <a href="/A362136/a362136.png">Scatterplot of a(n)</a>, n = 1..47545.
%e A362136 A360179 read as an irregular triangle of subsequences whose terms are nondecreasing.
%e A362136    n: row n of A360179    a(n)
%e A362136   ----------------------------
%e A362136    1: 1;                    1
%e A362136    2: 1, 2;                 2
%e A362136    3: 2, 3;                 2
%e A362136    4: 2, 4;                 2
%e A362136    5: 3, 5;                 2
%e A362136    6: 2, 4,  6;             3
%e A362136    7: 4, 6,  8;             3
%e A362136    8: 4, 7;                 2
%e A362136    9: 2, 5,  7, 10;         4
%e A362136   10: 4, 7, 10, 12;         4
%e A362136   11: 6, 8, 12, 16;         4
%e A362136   12: 5, 9;                 2
%e A362136   etc.
%t A362136 nn = 960;
%t A362136 c[_] := False; m = h[_] := 0; f[n_] := DivisorSigma[0, n];
%t A362136 a[1] = j = u = w = 1;
%t A362136 {1}~Join~Rest@ Reap[Do[
%t A362136       If[c[j],
%t A362136          k = j + f[u]; h[j]++; h[u]--,
%t A362136          k = f[j]; c[j] = True; h[j]++; Sow[n - 1 - m]; Set[m, n - 1] ];
%t A362136       u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
%t A362136       While[h[u] == 0, u++], {n, 2, nn}] ][[-1, -1]]
%Y A362136 Cf. A360179, A362134, A362135.
%K A362136 nonn
%O A362136 1,2
%A A362136 _Michael De Vlieger_, Apr 10 2023