math/totient.hpp

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• Last update: 2023-02-06 17:52:27+09:00
• Include: #include "math/totient.hpp"

Depends on

• math/prime_factor.hpp

Verified with

• verify/aoj_ntl/aoj_ntl_1_d.test.cpp

Code

#pragma once

#include "math/prime_factor.hpp"

long long totient(long long n) {
    auto pf = prime_factor(n);
    for (auto &[p, e] : pf) {
        n /= p;
        n *= p - 1;
    }
    return n;
}

#line 2 "math/totient.hpp"

#line 2 "math/prime_factor.hpp"

std::map<long long, int> prime_factor(long long n) {
    std::map<long long, int> res;
    for (long long i = 2; i * i <= n; i++) {
        while (n % i == 0) {
            res[i]++;
            n /= i;
        }
    }
    if (n != 1) res[n]++;
    return res;
}
#line 4 "math/totient.hpp"

long long totient(long long n) {
    auto pf = prime_factor(n);
    for (auto &[p, e] : pf) {
        n /= p;
        n *= p - 1;
    }
    return n;
}

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