We all know the Super Powers ofthis world and how they manage to get advantages in political warfare or evenin other sectors. But this is not a political platform and so we will talkabout a different kind of super powers – “The Super Power Numbers”. A positivenumber
is said to be super power when it is the power of at least two differentpositive integers. For example 64 is a super power as 64 = 8² and 64=  4³.You have to write a program that lists all super powers within 1 and 2⁶⁴-1 (inclusive).

Input

This program has noinput.

Output

Print all theSuper Power Numbers within 1 and 2^64 -1. Each line contains a single superpower number and the numbers are printed in ascending order.

ProblemSetter: Shahriar Manzoor, Special Thanks: Sohel Hafiz

题意：如果一个数是超级幂的话，那么它至少是两个不同正整数的幂，从小到大输出所有

思路：如果这个数是超级幂的话，那么它的指数一定是合数，如果我们先枚举底数，大小为1～（1<<16），然后在2^64-1的范围内找数

#include <iostream>
#include <cstring>
#include <algorithm>
#include <set>
#include <cstdio>
#include <cmath>
typedef unsigned long long ll;
using namespace std;
const int maxn = 100;

int vis[maxn];

int main() {
	memset(vis, 0, sizeof(vis));
	for (int i = 2; i < 100; i++)
		if (!vis[i]) {
			for (int j = i*i; j < 100; j += i)
				vis[j] = 1;
		}
	set<ll> ans;
	for (ll i = 2; i < (1<<16); i++) {
		int top = ceil(64*log10(2)/log10(i));
		ll tmp = 1;
		for (int j = 1; j < top; j++) {
			tmp *= i;
			if (vis[j])
				ans.insert(tmp);
		}
	}
	printf("1\n");
	set<ll>::iterator ite = ans.begin();
	while (ite != ans.end())
		cout << *ite++ << endl;
	return 0;
}

UVA - 11752 The Super Powers