The numbers k from sequence S000891.

1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 12, 11, 15, 16, 14, 18, 13, 20, 24, 21, 23, 30, 27, 25, 28, 32, 17, 36, 40, 22, 42, 45, 35, 48, 38, 41, 50, 33, 54, 60, 56, 26, 64, 63, 44, 72, 53, 80, 68, 70, 39, 84, 75, 49, 90, 66, 96, 81, 55, 52, 100, 108, 112, 95, 120, 19, 105

1

Note how some prime numbers take a long time to appear. Why?

T. D. Noe, Plot of 106 terms

T. D. Noe, Table of 106 terms

(Mma) nn = 10^6; t1 = Table[0, {Floor[Sqrt[nn]]}]; t2 = {}; found = 0; Do[c = Length[Select[Divisors[n], # <= Sqrt[n] &]]; If[c > 0 && c <= nn && t1[[c]] == 0, t1[[c]] = n; AppendTo[t2, {n, c}]; found++], {n, nn}]; Transpose[t2][[2]]

nonn

T. D. Noe, May 19 2016