Pairs (m,k) with increasing m such that m is the first number having k divisors <= sqrt(m).

1, 1, 4, 2, 12, 3, 24, 4, 36, 5, 60, 6, 120, 8, 180, 9, 192, 7, 240, 10, 360, 12, 576, 11, 720, 15, 840, 16, 900, 14, 1260, 18, 1296, 13, 1680, 20, 2520, 24, 2880, 21, 3600, 23, 5040, 30, 6300, 27, 6480, 25, 6720, 28, 7560, 32, 9216, 17, 10080, 36, 15120, 40

1

Note that each k appears only once. See S000892 and S000893 for the separate lists of m and k. This is sequence A038549 sorted and with k giving is position.

T. D. Noe, Plot of 106 pairs

T. D. Noe, Table of 106 pairs

(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}]; t2

nonn

T. D. Noe, May 19 2016