n-smooth   numbers are positive integers which have no prime factors  >  n.

The   n   (when using it in the expression)   n-smooth   is always prime,

there are   no   9-smooth numbers.

1   (unity)   is always included in n-smooth numbers.




2-smooth   numbers are non-negative powers of two.

5-smooth   numbers are also called   Hamming numbers.

7-smooth   numbers are also called    humble   numbers.



A way to express   11-smooth   numbers is:

  11-smooth  =  2i × 3j × 5k × 7m × 11p

           where     i, j, k, m, p ≥ 0  



Task

   calculate and show the first   25   n-smooth numbers   for   n=2   ───►   n=29
   calculate and show   three numbers starting with   3,000   n-smooth numbers   for   n=3   ───►   n=29
   calculate and show twenty numbers starting with  30,000   n-smooth numbers   for   n=503   ───►   n=521   (optional)


All ranges   (for   n)   are to be inclusive, and only prime numbers are to be used.

The (optional) n-smooth numbers for the third range are:   503,   509,   and   521.

Show all n-smooth numbers for any particular   n   in a horizontal list.

Show all output here on this page.



Related tasks

   Hamming numbers
   humble numbers


References

   Wikipedia entry:   Hamming numbers     (this link is re-directed to   Regular number).
   Wikipedia entry:   Smooth number
   OEIS entry:   A000079    2-smooth numbers or non-negative powers of two
   OEIS entry:   A003586    3-smooth numbers
   OEIS entry:   A051037    5-smooth numbers or Hamming numbers
   OEIS entry:   A002473    7-smooth numbers or humble numbers
   OEIS entry:   A051038   11-smooth numbers
   OEIS entry:   A080197   13-smooth numbers
   OEIS entry:   A080681   17-smooth numbers
   OEIS entry:   A080682   19-smooth numbers
   OEIS entry:   A080683   23-smooth numbers


func smooth_generator(primes) {
    var s = primes.len.of { [1] }
    {
        var n = s.map { .first }.min
        { |i|
            s[i].shift if (s[i][0] == n)
            s[i] << (n * primes[i])
        } * primes.len
        n
    }
}
 
for p in (primes(2,29)) {
    var g = smooth_generator(p.primes)
    say ("First 25 #{'%2d'%p}-smooth numbers: ", 25.of { g.run }.join(' '))
}
 
say ''
 
for p in (primes(3,29)) {
    var g = smooth_generator(p.primes)
    say ("3,000th through 3,002nd #{'%2d'%p}-smooth numbers: ", 3002.of { g.run }.last(3).join(' '))
}