F[0]=1; F[1]=1; F[n]=F[n div 2]+F[n div 3]+F[n div 5]+F[n div 7] with C

recursive_to_loop.c

#include <stdio.h>
#include <stdlib.h>

#define true 1
#define false 0

typedef struct {
  unsigned long long buff[65535];
  int size;
} collection;

void collection_init(collection *c) {
  c->size = 0;
}

void collection_add(collection *c, unsigned long long e) {
  c->buff[c->size] = e;
  c->size ++;
}

void collect_div(collection *c, int div, unsigned long long n) {
  unsigned long long div_r;
  div_r = n;
  while (true) {
    div_r /= div;
    if (div_r == 0 || div_r == 1) {
      collection_add(c, 1);
      break;
    }
    collection_add(c, div_r);
  }
}

unsigned long long loop_f(unsigned long long n) {
  collection c_2, c_3, c_5, c_7;
  collection_init(&c_2);
  collection_init(&c_3);
  collection_init(&c_5);
  collection_init(&c_7);

  collect_div(&c_2, 2, n);
  collect_div(&c_3, 3, n);
  collect_div(&c_5, 5, n);
  collect_div(&c_7, 7, n);
  
  unsigned long long sum = 0;
  int i2, i3, i5, i7;
  for (i2 = 0; i2 < c_2.size; i2++)
    for (i3 = 0; i3 < c_3.size; i3++)
      for (i5 = 0; i5 < c_5.size; i5++)
        for (i7 = 0; i7 < c_7.size; i7++)
          sum += c_2.buff[i2] + c_3.buff[i3] + c_5.buff[i5] + c_7.buff[i7];

  return sum;
}

int main(void) {
  unsigned long long n = 400000000000;
  printf("result: %llu\n", loop_f(n));
  return EXIT_SUCCESS;
}