DistinctPowers.java

package problem29;

/*
 Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:

 2^2=4,  2^3=8,   2^4=16,  2^5=32
 3^2=9,  3^3=27,  3^4=81,  3^5=243
 4^2=16, 4^3=64,  4^4=256, 4^5=1024
 5^2=25, 5^3=125, 5^4=625, 5^5=3125
 If they are then placed in numerical order, with any repeats removed, we get the
 following sequence of 15 distinct terms:

 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

 How many distinct terms are in the sequence generated by a^b for
 2 <= a <= 100 and 2 <= b <= 100?
 */

import java.math.BigInteger;
import java.util.HashSet;
import java.util.Set;

public class DistinctPowers {
   public static void main(String[] args) {
      System.out.println(sumPowers(100, 100));
   }
   
   private static int sumPowers(int limitA, int limitB) {
      Set<BigInteger> terms = new HashSet<BigInteger>();
      for(int i = 2; i <= limitA; i++) {
         for(int j = 2; j <= limitB; j++) {
            terms.add(BigInteger.valueOf(i).pow(j));
         }
      }
      return terms.size();
   }
}