Generate an array having sum of Euler Totient Function of all elements equal to N Last Updated : 17 Jan, 2022 Summarize Suggest changes Share Like Article Like Report Given a positive integer N, the task is to generate an array such that the sum of the Euler Totient Function of each element is equal to N. Examples: Input: N = 6Output: 1 6 2 3 Input: N = 12Output: 1 12 2 6 3 4 Approach: The given problem can be solved based on the divisor sum property of the Euler Totient Function, i.e., The Euler Totient Function of a number N< is the number of integers from 1 to N that gives GCD(i, N) as 1 and a number N can be represented as the summation of the Euler Totient Function values of all the divisors of N.Therefore, the idea is to find the divisors of the given number N as the resultant array. Below is the implementation of the above approach: C++ // C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to construct the array such // the sum of values of Euler Totient // functions of all array elements is N void constructArray(int N) { // Stores the resultant array vector<int> ans; // Find divisors in sqrt(N) for (int i = 1; i * i <= N; i++) { // If N is divisible by i if (N % i == 0) { // Push the current divisor ans.push_back(i); // If N is not a // perfect square if (N != (i * i)) { // Push the second divisor ans.push_back(N / i); } } } // Print the resultant array for (auto it : ans) { cout << it << " "; } } // Driver Code int main() { int N = 12; // Function Call constructArray(N); return 0; } Java // Java program for the above approach import java.util.*; class GFG{ // Function to construct the array such // the sum of values of Euler Totient // functions of all array elements is N static void constructArray(int N) { // Stores the resultant array ArrayList<Integer> ans = new ArrayList<Integer>(); // Find divisors in sqrt(N) for(int i = 1; i * i <= N; i++) { // If N is divisible by i if (N % i == 0) { // Push the current divisor ans.add(i); // If N is not a // perfect square if (N != (i * i)) { // Push the second divisor ans.add(N / i); } } } // Print the resultant array for(int it : ans) { System.out.print(it + " "); } } // Driver Code public static void main(String[] args) { int N = 12; // Function Call constructArray(N); } } // This code is contributed by splevel62 Python3 # Python3 program for the above approach from math import sqrt # Function to construct the array such # the sum of values of Euler Totient # functions of all array elements is N def constructArray(N): # Stores the resultant array ans = [] # Find divisors in sqrt(N) for i in range(1, int(sqrt(N)) + 1, 1): # If N is divisible by i if (N % i == 0): # Push the current divisor ans.append(i) # If N is not a # perfect square if (N != (i * i)): # Push the second divisor ans.append(N / i) # Print the resultant array for it in ans: print(int(it), end = " ") # Driver Code if __name__ == '__main__': N = 12 # Function Call constructArray(N) # This code is contributed by ipg2016107 C# // C# program for the above approach using System; using System.Collections.Generic; class GFG{ // Function to construct the array such // the sum of values of Euler Totient // functions of all array elements is N static void constructArray(int N) { // Stores the resultant array List<int> ans = new List<int>(); // Find divisors in sqrt(N) for(int i = 1; i * i <= N; i++) { // If N is divisible by i if (N % i == 0) { // Push the current divisor ans.Add(i); // If N is not a // perfect square if (N != (i * i)) { // Push the second divisor ans.Add(N / i); } } } // Print the resultant array foreach(int it in ans) { Console.Write(it + " "); } } // Driver Code public static void Main() { int N = 12; // Function Call constructArray(N); } } // This code is contributed by ukasp JavaScript <script> // javascript program for the above approach // Function to construct the array such // the sum of values of Euler Totient // functions of all array elements is N function constructArray(N) { // Stores the resultant array var ans = []; // Find divisors in sqrt(N) for(var i = 1; i * i <= N; i++) { // If N is divisible by i if (N % i == 0) { // Push the current divisor ans.push(i); // If N is not a // perfect square if (N != (i * i)) { // Push the second divisor ans.push(N / i); } } } // Print the resultant array document.write(ans); } // Driver Code var N = 12; // Function Call constructArray(N); // This code contributed by shikhasingrajput </script> Output: 1 12 2 6 3 4 Time Complexity: O(√N)Auxiliary Space: O(N) Advertise with us Next Article Count all possible values of K less than Y such that GCD(X, Y) = GCD(X+K, Y) K kiranu941 Follow Similar Reads Euler Totient for Competitive Programming What is Euler Totient function(ETF)?Euler Totient Function or Phi-function for 'n', gives the count of integers in range '1' to 'n' that are co-prime to 'n'. 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