Count of integers up to N which are non divisors and non coprime with N

Given an integer N, the task is to find the count of all possible integers less than N satisfying the following properties:

• The number is not coprime with N i.e their GCD is greater than 1.
• The number is not a divisor of N.

Examples:

Input: N = 10 
Output: 3 
Explanation: 
All possible integers which are less than 10 and are neither divisors nor coprime with 10, are {4, 6, 8}. 
Therefore, the required count is 3.
Input: N = 42 
Output: 23

Approach: 
Follow the steps below to solve the problem:

• Set count = N.
• Calculate Euler’s Totient function for all values up to N to find the count of numbers in the range [1, N] that are coprime to N, i.e., the numbers whose GCD (Greatest Common Divisor) with N is 1.
• Since these are coprime with N, subtract them from the count.
• Calculate the count of divisors of N using Sieve of Eratosthenes. Subtract them from count.
• Print the final value of count which is equal to:

Total count = N - Euler's totient(N) - Divisor count(N)

Below is the implementation of the above approach:

23

Time Complexity: O(N*log(log(N))) 
Auxiliary Space: O(N)