A362131 a(n) = smallest missing number u in A360179(1..n).

2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21

Offset: 1

Author

Michael De Vlieger, Apr 10 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..40000
• Michael De Vlieger, Labeled scatterplot of A360179(n), n = 1..300, showing a(n) in small red dots, and A360179(n) in large red when A360179(n) = a(n-1).

Crossrefs

Cf. A000005, A360179, A362132.

Programs

Mathematica

nn = 120; c[] := False; q[] := False; h[] := 0; f[n] := DivisorSigma[0, n];
a[1] = j = u = w = 1;
{2}~Join~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], q[k], j}, {k, True, k}];
     While[h[u] == 0, u++]; If[k == w, While[q[w], w++]];
     Sow[w], {n, 2, nn}] ][[-1, -1]]