A362127 Records in A360179.

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, 65, 69, 75, 77, 79, 80, 84, 86, 98, 99, 102, 105, 107, 119, 129, 130, 141, 143, 146, 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

Offset: 1

Author

Michael De Vlieger, Apr 09 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..8238
• Michael De Vlieger, Labeled scatterplot of m = A360179(n) 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.

Crossrefs

Cf. A000005, A360179, A362128.

Programs

Mathematica

nn = 10^4; c[] := False; h[] := 0; f[n_] := DivisorSigma[0, n];
a[1] = j = u = 1; r = 0;
Reap[Do[
    If[c[j],
      k = j + f[u]; h[j]++; h[u]--,
      k = f[j]; c[j] = True; h[j]++ ];
    u = Min[u, j]; Set[{a[n], j}, {k, k}]; While[h[u] == 0, u++];
    If[k > r, r = k; Sow[r]], {n, 2, nn}] ][[-1, -1]]