eulers totient function finds the number of relative primes of a number n from 1 to n n 10 totientcalculation totientn for i in range1 n printfi has totientcalculationi relative primes 1 has 0 relative primes 2 has 1 relative primes 3 has 2 relative primes 4 has 2 relative primes 5 has 4 relative primes 6 has 2 relative primes 7 has 6 relative primes 8 has 4 relative primes 9 has 6 relative primes eulers totient function finds the number of relative primes of a number n from 1 to n n 10 totient_calculation totient n for i in range 1 n print f i has totient_calculation i relative primes 1 has 0 relative primes 2 has 1 relative primes 3 has 2 relative primes 4 has 2 relative primes 5 has 4 relative primes 6 has 2 relative primes 7 has 6 relative primes 8 has 4 relative primes 9 has 6 relative primes
def totient(n: int) -> list:
    
    is_prime = [True for i in range(n + 1)]
    totients = [i - 1 for i in range(n + 1)]
    primes = []
    for i in range(2, n + 1):
        if is_prime[i]:
            primes.append(i)
        for j in range(len(primes)):
            if i * primes[j] >= n:
                break
            is_prime[i * primes[j]] = False

            if i % primes[j] == 0:
                totients[i * primes[j]] = totients[i] * primes[j]
                break

            totients[i * primes[j]] = totients[i] * (primes[j] - 1)

    return totients


if __name__ == "__main__":
    import doctest

    doctest.testmod()