思路來源：http://www.cnblogs.com/jhz033/p/7246028.html

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 7;
const int Mod = 1e9 + 7;
int a[maxn], ans[maxn], cnt[maxn], num[maxn];
ll quick_mod(ll a, ll b)
{
    ll ans = 1;
    while(b)
    {
        if(b&1) ans = ans*a%Mod;
        b /= 2;
        a = a*a%Mod;
    }
    return ans;
}
int main()
{
    int n, t, ca = 1, x;
    scanf("%d", &t);
    while(t--)
    {
        memset(a, 0, sizeof(a));
        memset(cnt, 0, sizeof(cnt));
        memset(ans, 0, sizeof(ans));
        scanf("%d", &n);
        for(int i = 1; i <= n; i++)  //桶裝
        {
            scanf("%d", &x);
            a[x]++;
        }
        for(int i = 1; i < maxn; i++)
            cnt[i] = cnt[i-1]+a[i];
        for(int i = 2; i < maxn; i++)  //列舉gcd
        {
            num[i] = 1;
            for(int j = 0; j < maxn; j += i)  //分段
            {
                int res, limit = j+i-1 >= maxn ? maxn-1 : j+i-1;
                if(!j) res = cnt[limit];
                else res = cnt[limit]-cnt[j-1];
                int tmp = j/i;
                if(!tmp && res) num[i] = 0;
                else if(res) num[i] = num[i]*quick_mod(tmp, res)%Mod;
            }
        }
        for(int i = maxn-1; i >= 2; i--)  //容斥
        {
            ans[i] = num[i];
            for(int j = i+i; j <= maxn-1; j += i)  //容斥
                ans[i] = ((ans[i]-ans[j])%Mod+Mod)%Mod;
        }
        ll res = 0;
        for(int i = 2; i <= maxn-1; i++)
            res += ans[i], res %= Mod;
        printf("Case #%d: %lld\n",ca++,res);
    }
    return 0;
}