Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.



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



See also
 OEIS:A069654


Related tasks
 Sequence: smallest number with exactly n divisors
 Sequence: nth number with exactly n divisors‎‎


res = {#, DivisorSigma[0, #]} & /@ Range[100000];
highest = 0;
filter = {};
Do[
 If[r[[2]] == highest + 1,
  AppendTo[filter, r[[1]]];
  highest = r[[2]]
  ]
 ,
 {r, res}
 ]
Take[filter, 15]