Humble numbers are positive integers which have   no   prime factors    >    7.



Humble numbers are also called   7-smooth numbers,   and sometimes called   highly composite,

although this conflicts with another meaning of   highly composite numbers.



Another way to express the above is:

  humble  =  2i × 3j × 5k × 7m 

           where     i, j, k, m ≥ 0 



Task

   show the first   50   humble numbers   (in a horizontal list)
   show the number of humble numbers that have   x   decimal digits for all   x's   up to   n   (inclusive).
   show   (as many as feasible or reasonable for above)   on separate lines
   show all output here on this page


Related tasks

   Hamming numbers


References

   Wikipedia: Smooth numbers, see the 2nd paragraph.
   OEIS A002473: humble numbers
   University of Ulm, The first 5842 terms of humble 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
    }
}
 
with (smooth_generator([2,3,5,7])) {|g|
    say 50.of { g.run }.join(' ')
}
 
say "\nThe digit counts of humble numbers"
say '═'*35
 
with (smooth_generator([2,3,5,7])) {|g|
    for (var(d=1,c=0); d <= 20; ++c) {
        var n = g.run
        n.len > d || next
        say "#{'%10s'%c.commify}  have  #{'%2d'%d}  digit#{[:s,''][d==1]}"
        (c, d) = (0, n.len)
    }
}