A Tau number is a positive integer divisible by the count of its positive divisors.



Task
Show the first   100   Tau numbers.
The numbers shall be generated during run-time (i.e. the code may not contain string literals, sets/arrays of integers, or alike).



Related task
  Tau function


def count(s): reduce s as $x (0; .+1);
 
# For pretty-printing
def nwise($n):
  def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
  n;
 
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;