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


import std.conv;
import std.stdio;
 
bool isHumble(int i) {
    if (i <= 1) return true;
    if (i % 2 == 0) return isHumble(i / 2);
    if (i % 3 == 0) return isHumble(i / 3);
    if (i % 5 == 0) return isHumble(i / 5);
    if (i % 7 == 0) return isHumble(i / 7);
    return false;
}
 
void main() {
    auto limit = short.max;
    int[int] humble;
    auto count = 0;
    auto num = 1;
 
    while (count < limit) {
        if (isHumble(num)) {
            auto str = num.to!string;
            auto len = str.length;
            humble[len]++;
            if (count < 50) write(num, ' ');
            count++;
        }
        num++;
    }
    writeln('\n');
 
    writeln("Of the first ", count, " humble numbers:");
    num = 1;
    while (num < humble.length - 1) {
        if (num in humble) {
            auto c = humble[num];
            writefln("%5d have %2d digits", c, num);
            num++;
        } else {
            break;
        }
    }
}