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import java.util.ArrayList;
class Achilles{
private static final double EPSILON = 1e-15;
private static ArrayList primeFactors(long n){
ArrayList factors = new ArrayList();
while (n % 2 == 0){
factors.add(new Long(2));
n = n / 2;
}
for(long i = 3; i <= Math.sqrt(n); i = i + 2){
while (n % i == 0){
factors.add(new Long(i));
n = n / i;
}
}
if(n > 2)
factors.add(new Long(n));
return factors;
}
private static boolean isAchilles(int n){
ArrayList factors = primeFactors(n);
for(int i = 0; i < factors.size(); i++){
if(n % Math.pow(((Long)factors.get(i)).longValue() + 0.0, 2) != 0)
return false;
}
for(int i = 2; i <= Math.sqrt(n); i++) {
double d = Math.log(n) / Math.log(i);
if(Math.abs(d - Math.round(d)) < EPSILON)
return false;
}
return true;
}
public static ArrayList nAchilles(int n){
ArrayList achilles = new ArrayList();
int i = 1;
do{
i++;
if(isAchilles(i))
achilles.add(new Integer(i));
}while(achilles.size() < n);
return achilles;
}
public static void main(String[] args){
ArrayList achilles = Achilles.nAchilles(20);
for(int i = 0; i < achilles.size() - 1; i++){
System.out.print(achilles.get(i) + ", ");
}
System.out.println(achilles.get(achilles.size() - 1));
}
}
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