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


import Foundation
 
// See https://en.wikipedia.org/wiki/Divisor_function
func divisorCount(number: Int) -> Int {
    var n = number
    var total = 1
    // Deal with powers of 2 first
    while (n & 1) == 0 {
        total += 1
        n >>= 1
    }
    // Odd prime factors up to the square root
    var p = 3
    while p * p <= n {
        var count = 1
        while n % p == 0 {
            count += 1
            n /= p
        }
        total *= count
        p += 2
    }
    // If n > 1 then it's prime
    if n > 1 {
        total *= 2
    }
    return total
}
 
let limit = 100
print("The first \(limit) tau numbers are:")
var count = 0
var n = 1
while count < limit {
    if n % divisorCount(number: n) == 0 {
        print(String(format: "%5d", n), terminator: "")
        count += 1
        if count % 10 == 0 {
            print()
        }
    }
    n += 1
}