51nod 1227

杜教筛

#include 
using namespace std;
typedef long long ll;

const int N = 1000001;
const ll mod = 1e9 + 7;
const ll inv = (mod + 1) / 2;
const ll _6 = (mod + 1) / 6;
const int mo = 2333333;

bool isPrime[N];
ll phi[N];
int prime[N];
int cnt;

void init()
{
    memset(isPrime, true, sizeof isPrime);
    phi[1] = 1;
    for(int i = 2; i < N; ++i)
    {
        if(isPrime[i])
        {
            prime[++cnt] = i;
            phi[i] = i - 1;
        }
        for(int j = 1; j <= cnt && i * prime[j] < N; ++j)
        {
            isPrime[i * prime[j]] = false;
            if(i % prime[j] == 0)
            {
                phi[i * prime[j]] = phi[i] * prime[j];
                break;
            }
            phi[i * prime[j]] = phi[i] * (prime[j] - 1);
        }
    }
    for(ll i = 2; i < N; ++i)
        phi[i] = (i * phi[i] + phi[i - 1]) % mod;
}



int last[mo], next[mo];
ll t[mo], v[mo];
int l;

void add(int x, ll y, ll z)
{
    t[++l] = y;
    next[l] = last[x];
    last[x] = l;
    v[l] = z;
}
ll cal(ll x)
{
    if(x < N) return phi[x];
    int k = x % mo;
    for(int i = last[k]; i; i = next[i])
        if(t[i] == x) return v[i];
    ll res = x * (x + 1) % mod * ((x * 2 + 1) % mod) % mod * _6 % mod;
    ll r;
    for(ll i = 2; i <= x; i = r + 1)
    {
        ll tmp = x / i;
        r = x / tmp;
        res = ((res - cal(tmp) * (r - i + 1) % mod * ((r + i) % mod) % mod * inv % mod) % mod + mod) % mod;
    }
    add(k, x, res);
    return res;
}
ll Calc(ll x)
{
    ll res = x;
    ll r;
    for(ll i = 1; i <= x; i = r + 1)
    {
        ll tmp = x / i;
        r = x / tmp;
        res = (res + cal(tmp) * (r - i + 1) % mod) % mod;
    //    cout << res << endl;
    }
    res = res * inv % mod;
  //  ll t = x % mod * ((x + 1) % mod) % mod * inv % mod;
    return res;
}
int main()
{
    init();
    ll l, r;
    cin >> l >> r;
    cout << ((Calc(r) - Calc(l - 1)) % mod + mod) % mod << endl;
    return 0;
}