给定两个整数M和K ，任务是计算[0，M]之间的整数数，以使该整数中M的GCD等于K。
例子：
Input: M = 9, K = 1
Output: 6
Explanation:
The possible numbers such that when paired with 9, there GCD is 1, are 1, 2, 4, 5, 7, 8.
Input: M = 10, K = 5
Output: 1
方法：
- GCD为K且M为M的整数的形式为K，2K，3K等，依此类推，直到M。
- 让我们考虑K的系数，即1、2、3、4…直到(M / K)。
- 现在我们只需要找到GCD的(M / K)= 1的系数的数量即可。所以现在问题减少了，找到了Gcd为(m / k)的1到(M / K)之间的整数。 )= 1。
- 为了找到这个，我们将使用(M / K)的Euler totient函数。
下面是上述方法的实现：
C++
// C++ program to Count of numbers
// between 0 to M which have GCD
// with M equals to K.
#include
using namespace std;
// Function to calculate GCD
// using euler totient function
int EulerTotientFunction(int limit)
{
int copy = limit;
// Finding the prime factors of
// limit to calculate it's
// euler totient function
vector primes;
for (int i = 2; i * i <= limit; i++) {
if (limit % i == 0) {
while (limit % i == 0) {
limit /= i;
}
primes.push_back(i);
}
}
if (limit >= 2) {
primes.push_back(limit);
}
// Calculating the euler totien
// function of (m/k)
int ans = copy;
for (auto it : primes) {
ans = (ans / it) * (it - 1);
}
return ans;
}
// Function print the count of
// numbers whose GCD with M
// equals to K
void CountGCD(int m, int k)
{
if (m % k != 0) {
// GCD of m with any integer
// cannot be equal to k
cout << 0 << endl;
return;
}
if (m == k) {
// 0 and m itself will be
// the only valid integers
cout << 2 << endl;
return;
}
// Finding the number upto which
// coefficient of k can come
int limit = m / k;
int ans = EulerTotientFunction(limit);
cout << ans << endl;
}
// Driver code
int main()
{
int M = 9;
int K = 1;
CountGCD(M, K);
return 0;
} Java
// Java program to Count of numbers
// between 0 to M which have GCD
// with M equals to K.
import java.util.*;
class GFG{
// Function to calculate GCD
// using euler totient function
static int EulerTotientFunction(int limit)
{
int copy = limit;
// Finding the prime factors of
// limit to calculate it's
// euler totient function
Vector primes = new Vector();
for (int i = 2; i * i <= limit; i++) {
if (limit % i == 0) {
while (limit % i == 0) {
limit /= i;
}
primes.add(i);
}
}
if (limit >= 2) {
primes.add(limit);
}
// Calculating the euler totien
// function of (m/k)
int ans = copy;
for (int it : primes) {
ans = (ans / it) * (it - 1);
}
return ans;
}
// Function print the count of
// numbers whose GCD with M
// equals to K
static void CountGCD(int m, int k)
{
if (m % k != 0) {
// GCD of m with any integer
// cannot be equal to k
System.out.print(0 +"\n");
return;
}
if (m == k) {
// 0 and m itself will be
// the only valid integers
System.out.print(2 +"\n");
return;
}
// Finding the number upto which
// coefficient of k can come
int limit = m / k;
int ans = EulerTotientFunction(limit);
System.out.print(ans +"\n");
}
// Driver code
public static void main(String[] args)
{
int M = 9;
int K = 1;
CountGCD(M, K);
}
}
// This code is contributed by sapnasingh4991 Python3
# Python3 program to Count of numbers
# between 0 to M which have GCD
# with M equals to K.
# Function to calculate GCD
# using euler totient function
def EulerTotientFunction(limit):
copy = limit
# Finding the prime factors of
# limit to calculate it's
# euler totient function
primes = []
for i in range(2, limit + 1):
if i * i > limit:
break
if (limit % i == 0):
while (limit % i == 0):
limit //= i
primes.append(i)
if (limit >= 2):
primes.append(limit)
# Calculating the euler totien
# function of (m//k)
ans = copy
for it in primes:
ans = (ans // it) * (it - 1)
return ans
# Function print the count of
# numbers whose GCD with M
# equals to K
def CountGCD(m, k):
if (m % k != 0):
# GCD of m with any integer
# cannot be equal to k
print(0)
return
if (m == k):
# 0 and m itself will be
# the only valid integers
print(2)
return
# Finding the number upto which
# coefficient of k can come
limit = m // k
ans = EulerTotientFunction(limit)
print(ans)
# Driver code
if __name__ == '__main__':
M = 9
K = 1
CountGCD(M, K)
# This code is contributed by mohit kumar 29C#
// C# program to Count of numbers
// between 0 to M which have GCD
// with M equals to K.
using System;
using System.Collections.Generic;
class GFG{
// Function to calculate GCD
// using euler totient function
static int EulerTotientFunction(int limit)
{
int copy = limit;
// Finding the prime factors of
// limit to calculate it's
// euler totient function
List primes = new List();
for (int i = 2; i * i <= limit; i++)
{
if (limit % i == 0)
{
while (limit % i == 0)
{
limit /= i;
}
primes.Add(i);
}
}
if (limit >= 2)
{
primes.Add(limit);
}
// Calculating the euler totien
// function of (m/k)
int ans = copy;
foreach (int it in primes)
{
ans = (ans / it) * (it - 1);
}
return ans;
}
// Function print the count of
// numbers whose GCD with M
// equals to K
static void CountGCD(int m, int k)
{
if (m % k != 0)
{
// GCD of m with any integer
// cannot be equal to k
Console.Write(0 + "\n");
return;
}
if (m == k)
{
// 0 and m itself will be
// the only valid integers
Console.Write(2 + "\n");
return;
}
// Finding the number upto which
// coefficient of k can come
int limit = m / k;
int ans = EulerTotientFunction(limit);
Console.Write(ans + "\n");
}
// Driver code
public static void Main(String[] args)
{
int M = 9;
int K = 1;
CountGCD(M, K);
}
}
// This code is contributed by PrinciRaj1992 输出：
6