Generate an array having sum of Euler Totient Function of all elements equal to N

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 = 6
Output: 1 6 2 3

Input: N = 12
Output: 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:

1 12 2 6 3 4

Time Complexity: O(√N)
Auxiliary Space: O(N)