Problem with SPOJ GCDEX

#	User	Rating
1	tourist	4009
2	jiangly	3823
3	Benq	3738
4	Radewoosh	3633
5	jqdai0815	3620
6	orzdevinwang	3529
7	ecnerwala	3446
8	Um_nik	3396
9	ksun48	3390
10	gamegame	3386

#	User	Contrib.
1	cry	166
2	maomao90	163
2	Um_nik	163
4	atcoder_official	161
5	adamant	159
6	-is-this-fft-	158
7	awoo	157
8	TheScrasse	154
9	nor	153
9	Dominater069	153

I was solving this problem. The formula for this problem can be founded here. I've stress tested my code, and found out that this is the smallest test case where my code failed (answer for n <= 225537 are all correct).

Input

Output

Expect

It is obvious that my output is wrong, since $$$answer(n) > answer(n-1)$$$. I have no idea why my code doesn't work.

Code

#include <bits/stdc++.h>
using namespace std;

const int N = 1e6 + 5;

bool isprime[N];
vector<int> prime;
int mobius[N];
int phi[N];
int phi_pref[N];

void init() {
	fill(isprime, isprime + N, true);
	isprime[0] = isprime[1] = false;
	mobius[1] = 1;
	phi[1] = 1;
	for(int i = 2; i < N; ++i) {
		if(isprime[i]) {
			prime.push_back(i);
			mobius[i] = -1;
			phi[i] = i - 1;
		}
		for(auto& p : prime) {
			if(p * i >= N) {
				break;
			}
			isprime[p * i] = false;
			mobius[p * i] = mobius[p] * mobius[i];
			phi[p * i] = phi[p] * phi[i];
			if(i % p == 0) {
				mobius[p * i] = 0;
				phi[p * i] = phi[i] * p;
				break;
			}
		}
	}
	for(int i = 1; i < N; ++i) {
		phi_pref[i] = phi_pref[i - 1] + phi[i];
	}
}

int main(int argc, char* argv[]) {
	ios::sync_with_stdio(false);
	cin.tie(0);
	init();
	int n;
	while(cin >> n && n) {
		long long ans = 0;
		for(int i = 1, j; i <= n; i = j) {
			int p = n / i;
			j = n / p + 1;
			ans += 1LL * p * (p - 1) / 2 * (phi_pref[j - 1] - phi_pref[i - 1]);
		}
		cout << ans << "\n";
	}
	return 0;
}

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