The numbers m from sequence S000894.
1, 4, 12, 24, 36, 60, 120, 180, 192, 240, 360, 576, 720, 840, 900, 1260, 1296, 1680, 2520, 2880, 3600, 5040, 6300, 6480, 6720, 7560, 9216, 10080, 15120, 15360, 20160, 25200, 25920, 27720, 32400, 44100, 45360, 46080, 50400, 55440, 60480, 61440, 83160, 100800
1
As expected these numbers have many small factors. The first number having n prime factors is 2, 6, 60, 840, 27720, 720720, which appears to be sequence A086332.
T. D. Noe, Plot of 105 terms
T. D. Noe, Table of 105 terms
(Mma) nn = 10^6; t3 = Table[0, {Floor[Sqrt[nn]]}]; t4 = {}; found = 0; Do[c = Length[Select[Divisors[n], # < Sqrt[n] &]]; If[c > 0 && c <= nn && t3[[c]] == 0, t3[[c]] = n; AppendTo[t4, {n, c}]; found++], {n, nn}]; Transpose[t4][[1]]
Cf. A086332, A227068, S000891-S000896.
nonn
T. D. Noe, May 19 2016