Number of Divisor of a Number using Prime Factorization

#include<bits/stdc++.h>
#define max_num 1000007
using namespace std;
int marking[1000007+5];
vector<int> storage;
void prime_number(){
	for(int i=2;i<=max_num;i++){
		if(marking[i]==0){
			for(int j=i+i;j<=max_num;j=j+i){
				marking[j]=1;
			}
		}
	}
	for(int i=2;i<=max_num;i++){
		if(marking[i]==0){
			storage.push_back(i);
		}
	}
	sort(storage.begin(),storage.end());
}
int main()
{
	prime_number();
	int test_case,case_no=0;
	scanf("%d",&test_case);
	while(test_case--){
		long long number; cin>>number;
		int counting,total=1;
		for(int i=0;i<storage.size() and storage[i]<=sqrt(number);i++){
			counting=0;
			if(number<storage[i]) break;
			while(number%storage[i]==0){
				number=number/storage[i];
				counting++;
			}
			total=total*(counting+1);
		}
		if(number>1) total=total*2;
		printf("Case %d: %d\n",++case_no,total-1);
	}
}