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43 lines
1.2 KiB
Java
43 lines
1.2 KiB
Java
package com.jwetherell.algorithms.mathematics;
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/**
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* In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled
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* co-prime)[1] if the only positive integer that divides both of them is 1. That is, the only common positive factor
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* of the two numbers is 1. This is equivalent to their greatest common divisor being 1.
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* <p>
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* http://en.wikipedia.org/wiki/Coprime_integers
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* <br>
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* @author Szymon Stankiewicz <mail@stankiewicz.me>
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* @author Justin Wetherell <phishman3579@gmail.com>
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*/
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public class Coprimes {
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private Coprimes() { }
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/**
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*
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* Euler's totient function. Because this function is multiplicative such implementation is possible.
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* <p>
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* Time complexity: O(sqrt(n))
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* <p>
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* @param n Long integer
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* @return number of coprimes smaller or equal to n
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*/
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public static long getNumberOfCoprimes(long n) {
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if(n < 1)
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return 0;
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long res = 1;
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for(int i = 2; i*i <= n; i++) {
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int times = 0;
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while(n%i == 0) {
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res *= (times > 0 ? i : i-1);
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n /= i;
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times++;
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}
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}
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if(n > 1)
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res *= n-1;
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return res;
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}
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}
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