【LG4397】[JLOI2014]聪明的燕姿

【LG4397】[JLOI2014]聪明的燕姿

题面

洛谷

题解

考虑到约数和函数\(\sigma = \prod (1+p_i+...+p_i^{r_i})\)，直接爆搜把所有数搜出来即可。

爆搜过程和这道题一样，这里不再赘述。

代码

#include <iostream> 
#include <cstdio> 
#include <cstdlib> 
#include <cstring> 
#include <cmath> 
#include <algorithm> 
using namespace std; 
const int MAX_N = 1e5 + 5; 
int prime[MAX_N], num;
bool nprime[MAX_N]; 
void sieve() { 
	for (int i = 2; i <= 1e5; i++) { 
		if (!nprime[i]) prime[++num] = i; 
		for (int j = 1; j <= num && prime[j] * i <= 1e5; j++) { 
			nprime[prime[j] * i] = 1; 
			if (i % prime[j] == 0) break; 
		} 
	} 
}
int Prime(int x) {
	if (x <= 1e5) return !nprime[x];
	for (int i = 1; i <= num && prime[i] * prime[i] <= x; i++)
		if (!(x % prime[i])) return 0;
	return 1;
}

int ans[MAX_N], cnt; 
void solve(int S, int n, int lst) { 
	if (S - 1 > prime[num] && Prime(S - 1)) ans[++cnt] = n * (S - 1); 
	for (int i = lst; i; i--) { 
		int sum = 1, times = prime[i]; 
		for (; sum + times <= S; ) { 
			sum += times; 
			if (S % sum == 0) solve(S / sum, n * times, i - 1); 
			if (1ll * times * prime[i] <= 1ll * S) times *= prime[i]; 
			else break; 
		} 
	} 
	if (S == 1) ans[++cnt] = n; 
} 
int S; 
int main () { 
#ifndef ONLINE_JUDGE 
    freopen("cpp.in", "r", stdin);
	freopen("cpp.out", "w", stdout); 
#endif 
	sieve(); 
	while (scanf("%d", &S) != EOF) { 
		cnt = 0; 
		solve(S, 1, num); 
		sort(&ans[1], &ans[cnt + 1]);
		printf("%d\n", cnt); 
		for (int i = 1; i <= cnt; i++) printf("%d ", ans[i]); 
		if (cnt) putchar('\n'); 
	} 
    return 0; 
}