Product of proper divisors of a number for Q queries

Last Updated : 27 Aug, 2020

Given an integer N, the task is to find the product of proper divisors of the number modulo 10⁹+ 7 for Q queries.

Examples:

Input: Q = 4, arr[] = { 4, 6, 8, 16 };
Output: 2 6 8 64
Explanation:
4 => 1, 2 = 1 * 2 = 2
6 => 1, 2, 3 = 1 * 2 * 3 = 6
8 => 1, 2, 4 = 1 * 2 * 4 = 8
16 => 1, 2, 4, 8 = 1 * 2 * 4 * 8 = 64

Input: arr[] = { 3, 6, 9, 12 }
Output: 1 6 3 144

Approach: The idea is to pre-compute and store product of proper divisors of elements with the help of Sieve of Eratosthenes.

Below is the implementation of the above approach:

C++

// C++ implementation of 
// the above approach 
  
#include <bits/stdc++.h> 
#define ll long long int 
#define mod 1000000007 
  
using namespace std; 
  
vector<ll> ans(100002, 1); 
  
// Function to precompute the product 
// of proper divisors of a number at 
// it's corresponding index 
void preCompute() 
{ 
    for (int i = 2; i <= 100000 / 2; i++) { 
        for (int j = 2 * i; j <= 100000; j += i) { 
            ans[j] = (ans[j] * i) % mod; 
        } 
    } 
} 
  
int productOfProperDivi(int num) 
{ 
  
    // Returning the pre-computed 
    // values 
    return ans[num]; 
} 
  
// Driver code 
int main() 
{ 
    preCompute(); 
    int queries = 5; 
    int a[queries] = { 4, 6, 8, 16, 36 }; 
  
    for (int i = 0; i < queries; i++) { 
        cout << productOfProperDivi(a[i]) 
             << ", "; 
    } 
    return 0; 
}

Java

// Java implementation of 
// the above approach 
import java.util.*; 
class GFG 
{ 
    static final int mod = 1000000007; 
  
    static long[] ans = new long[100002]; 
  
    // Function to precompute the product 
    // of proper divisors of a number at 
    // it's corresponding index 
    static void preCompute() 
    { 
        for (int i = 2; i <= 100000 / 2; i++)  
        { 
            for (int j = 2 * i; j <= 100000; j += i)  
            { 
                ans[j] = (ans[j] * i) % mod; 
            } 
        } 
    } 
  
    static long productOfProperDivi(int num) 
    { 
  
        // Returning the pre-computed 
        // values 
        return ans[num]; 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        Arrays.fill(ans, 1); 
        preCompute(); 
        int queries = 5; 
        int[] a = { 4, 6, 8, 16, 36 }; 
  
        for (int i = 0; i < queries; i++)  
        { 
            System.out.print(productOfProperDivi(a[i]) + ", "); 
        } 
    } 
} 
  
// This code is contributed by Rajput-Ji

Python3

# Python3 implementation of 
# the above approach 
mod = 1000000007
  
ans = [1] * (100002) 
  
# Function to precompute the product 
# of proper divisors of a number at 
# it's corresponding index 
def preCompute(): 
  
    for i in range(2, 100000 // 2 + 1): 
        for j in range(2 * i, 100001, i): 
            ans[j] = (ans[j] * i) % mod 
  
def productOfProperDivi(num): 
  
    # Returning the pre-computed 
    # values 
    return ans[num] 
  
# Driver code 
if __name__ == "__main__": 
  
    preCompute() 
    queries = 5
    a = [ 4, 6, 8, 16, 36 ] 
  
    for i in range(queries): 
        print(productOfProperDivi(a[i]), end = ", ") 
  
# This code is contributed by chitranayal 

C#

// C# implementation of 
// the above approach 
using System; 
  
class GFG{ 
      
static readonly int mod = 1000000007; 
  
static long[] ans = new long[100002]; 
  
// Function to precompute the product 
// of proper divisors of a number at 
// it's corresponding index 
static void preCompute() 
{ 
    for(int i = 2; i <= 100000 / 2; i++)  
    { 
        for(int j = 2 * i; j <= 100000; j += i)  
        { 
            ans[j] = (ans[j] * i) % mod; 
        } 
    } 
} 
  
static long productOfProperDivi(int num) 
{ 
  
    // Returning the pre-computed 
    // values 
    return ans[num]; 
} 
  
// Driver code 
public static void Main(String[] args) 
{ 
    for(int i = 0 ; i < 100002; i++) 
        ans[i] = 1; 
          
    preCompute(); 
  
    int queries = 5; 
    int[] a = { 4, 6, 8, 16, 36 }; 
  
    for(int i = 0; i < queries; i++)  
    { 
        Console.Write(productOfProperDivi(a[i]) + ", "); 
    } 
} 
} 
  
// This code is contributed by Princi Singh

Output:

2, 6, 8, 64, 279936,

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes

Related Articles

C++

Java

Python3

C#