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


#include <limits.h>
#include <stdbool.h>
#include <stdio.h>
#include <string.h>
 
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;
}
 
int main() {
    int limit = SHRT_MAX;
    int humble[16];
    int count = 0;
    int num = 1;
    char buffer[16];
 
    memset(humble, 0, sizeof(humble));
 
    for (; count < limit; num++) {
        if (isHumble(num)) {
            size_t len;
            sprintf_s(buffer, sizeof(buffer), "%d", num);
            len = strlen(buffer);
            if (len >= 16) {
                break;
            }
            humble[len]++;
 
            if (count < 50) {
                printf("%d ", num);
            }
            count++;
        }
    }
    printf("\n\n");
 
    printf("Of the first %d humble numbers:\n", count);
    for (num = 1; num < 10; num++) {
        printf("%5d have %d digits\n", humble[num], num);
    }
 
    return 0;
}