HackerRank - "Identify Smith Numbers"

I guess the punch line of this one is Sieving for primes.

#include <cmath>
#include <cstdio>
#include <climits>
#include <cctype>
#include <vector>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;

vector<int> primes;

int digiSum(int n)
{
    int ret = 0;
    while (n)
    {
        ret += n % 10;
        n /= 10;
    }
    return ret;
}

int facSum(int n)
{
    int ret = 0;
    
    int pinx = 0;
    while (n > 1 && pinx < primes.size())
    {
        int p = primes[pinx];
        while (n % p == 0)
        {
            n /= p;
            ret += digiSum(p);
        }
        pinx++;
    }
    if (n > 1)
    {
        ret += digiSum(n);
    }
    return ret;
}

void go(int n)
{
    int dSum = digiSum(n);
    int fSum = facSum(n);
    cout << (dSum == fSum ? 1 : 0) << endl;
}

void sieving(int n)
{
    int bound = ceil(sqrt(n));
    vector<bool> mark(bound + 1, true);

    int removed = 1;
    int picked = 2;
    while (removed)
    {
        removed = 0;
        for (int i = 2 * picked; i <= bound; i += picked)
        {
            mark[i] = false;
            removed++;
        }

        picked++;
        while (!mark[picked]) picked++;
    }    

    for (int i = 2; i < mark.size(); i ++)
        if (mark[i])
            primes.push_back(i);
}

int main() 
{
    sieving(INT_MAX);
    int n; cin >> n;
    go(n);
    return 0;
}