Expert · Number theory · 241 of 264
Euler's totient
Count how many numbers from 1 to n share no common divisor with n except 1. Use the prime factors of n (n up to 10^11).
Input: n. Output: phi(n).
Examples
Input
9
Output
6
Input
1
Output
1
Input
36
Output
12
2 more tests check other inputs when you press Check.
Stuck? The idea behind number theory
Whole-number tricks: n % d == 0 means d divides n; test divisors only up to the square root; the sieve of Eratosthenes finds every prime up to n at once.
pow(a, b, m) works out a to the power b, modulo m, quickly, even when the power is huge.
n = 50
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n ** 0.5) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
print(sum(is_prime))Watch for: Testing every number up to n one by one is too slow for big inputs: the hidden tests notice.