TheAlgorithms-C-Plus-Plus/math/eulers_totient_function.cpp

/// C++ Program to find Euler Totient Function
#include<iostream>

/*
 * Euler Totient Function is also known as phi function.
 * phi(n) = phi(p1^a1).phi(p2^a2)...
 * where p1, p2,... are prime factors of n.
 * 3 Euler's properties:
 * 1. phi(prime_no) = prime_no-1
 * 2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
 * 3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
 * Applying this 3 properties on the first equation.
 * phi(n) = n. (1-1/p1). (1-1/p2). ...
 * where p1,p2... are prime factors.
 * Hence Implementation in O(sqrt(n)).
 * phi(100) = 40
 * phi(1) = 1
 * phi(17501) = 15120
 * phi(1420) = 560
 */

// Function to caculate Euler's totient phi
int phiFunction(int n) {
    int result = n;
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            while (n % i == 0) {
                n /= i;
            }
            result -= result / i;
        }
    }
    if (n > 1) result -= result / n;
    return result;
}

int main() {
    int n;
    std::cin >> n;
    std::cout << phiFunction(n);
}