思路:

\(ans=\sum_{i \in \{x|n\%x=0\}}\phi(\frac{n}{i})\)


证明:

\(M=it\)

\(\Rightarrow t \leq \frac{n}{i} \And (\frac{n}{i},t)=1\)

\(So\ \ t\)的可行数量为\(\phi(\frac{n}{i})\)

答案为\(ans=\sum_{i \in \{x|n\%x=0\}}\phi(\frac{n}{i})\)

\(\mathfrak{Talk\ is\ cheap,show\ you\ the\ code.}\)

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
# define Type template<typename T>
# define read read1<int>()
Type inline T read1()
{
    T t=0;
    bool ty=0;
    char k;
    do k=getchar(),(k=='-')&&(ty=1);while('0'>k||k>'9');
    do t=(t<<3)+(t<<1)+(k^'0'),k=getchar();while('0'<=k&&k<='9');
    return ty?-t:t;
}
# define int long long
# define fre(k) freopen(k".in","r",stdin);freopen(k".out","w",stdout)
int work(int n)
{
    int tn=n;
    for(int i=2;i*i<=n;++i)
        if(!(n%i))
        {
            while(!(n%i))n/=i;
            tn=tn/i*(i-1);
        }
    if(n!=1)tn=tn/n*(n-1);
    return tn;
}
signed main()
{
    for(int T=read;T--;)
    {
        int s=read,m=read,ans=0;
        for(int i=1;i*i<=s;++i)
            if(!(s%i))
                if(i*i==s&&i>=m)ans+=work(i);
                else
                {
                    if(i>=m)ans+=work(s/i);
                    if(s/i>=m)ans+=work(i);
                }
        printf("%lld\n",ans);
    }
    return 0;
}
01-11 12:44