Codeforces 235E Number Challenge (莫比乌斯反演)

#include   
#include   
#include   
#include   
#include   
#include   
#include   
#include   
#include   
using namespace std;  


#define inf 0x3f3f3f3f
#define N 4000020
#define M 1000020
#define LL long long
#define mod 1073741824
#define ls (i << 1)
#define rs (ls | 1)
#define md (ll + rr >> 1)
#define lson ll, md, ls
#define rson md + 1, rr, rs
#define B 350


int p[N], cnt, s[N], d[N];
int mu[N], np[N];
int x[N];

void init() {
	s[1] = 1, mu[1] = 1;
	d[1] = 1;
	for(int i = 2; i < N; ++i) {
		if(!np[i]) {
			p[cnt++] = i;
			mu[i] = -1;
			d[i] = 2;
			s[i] = i;
		}
		for(int j = 0; j < cnt && i * p[j] < N; ++j) {
			int t = i * p[j];
			np[t] = 1;
			if(i % p[j] == 0) {
				mu[t] = 0;
				s[t] = s[i] * p[j];
				if(s[t] == t) d[t] = d[i] + 1;
				else d[t] = d[t/s[t]] * d[s[t]];
				break;
			}
			mu[t] = mu[i] * -1;
			s[t] = p[j];
			d[t] = d[i] * d[p[j]];
		}
	}
}




int a, b, c;

int main() {
	init();
	LL ans = 0;
	cin >> a >> b >> c;
	for(int i = 1; i <= a; ++i) {
		for(int j = 1; j <= b; ++j) {
			x[i*j]++;
		}
	}
	for(int i = 1; i <= c; ++i) {
		LL t1 = 0, t2 = 0;
		for(int j = 1; j <= c / i; ++j) {
			t1 += d[j];
			if(t1 >= mod) t1 -= mod;
		}
		for(int j = i; j <= a * b; j += i) {
			t2 += 1LL * d[j/i] * x[j] % mod;
			if(t2 >= mod) t2 -= mod;
		}
		ans += mu[i] * t1 % mod * t2 % mod;
		ans %= mod;
		if(ans < 0) ans += mod;
	}
	cout << ans << endl;
	return 0;
}