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


using Primes
 
function numfactors(n)
    f = [one(n)]
    for (p, e) in factor(n)
        f = reduce(vcat, [f * p^j for j in 1:e], init = f)
    end
    length(f)
end
 
function taunumbers(toget = 100)
    n = 0
    for i in 1:100000000
        if i % numfactors(i) == 0
            n += 1
            print(rpad(i, 5), n % 20 == 0 ? " \n" : "")
            n == toget && break
        end
    end
end
 
taunumbers()
 