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


 
load "stdlib.ring"
 
limit = 10
numList = []
 
for n2 = 0 to limit
    for n3 = 0 to limit
        for n5 = 0 to limit
            for n7 = 0 to limit
                num = pow(2,n2) * pow(3,n3) * pow(5,n5) * pow(7,n7)
                add(numList,num)
            next
        next
    next
next
 
numList = sort(numList)
 
see "The first 50 Humble numbers: " + nl
 
for n = 1 to 50
    see "" + numList[n] + " "
next
 