Calculate the sequence where each term an is the nth that has n divisors.

Task
Show here, on this page, at least the first 15 terms of the sequence.

See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
d = Table[
  Length[Divisors[n]], {n, 
   200000}]; t = {}; n = 0; ok = True; While[ok, n++; 
 If[PrimeQ[n], AppendTo[t, Prime[n]^(n - 1)], 
  c = Flatten[Position[d, n, 1, n]]; 
  If[Length[c] >= n, AppendTo[t, c[[n]]], ok = False]]]; 
t