Distinct powers: https://projecteuler.net/problem=29

DistinctPowers.java

class Entry {
  public final long base;
  public final long exponent;
  
  public Entry(long base, long exponent) {
    // 2⁷ > 100 so we start from the sixth power
    for (int e = 6; e > 1; --e) {
      final double pow = Math.pow(base, 1.0 / e);
      final long roundedPow = Math.round(pow);
      
      // Normalize the base and exponent
      if (pow == roundedPow) {
        base = roundedPow;
        exponent *= e;
        
        break;
      }
    }
    
    this.base = base;
    this.exponent = exponent;
  }
}

public class Solution {
  public int distinctPowers() {
    final Set<Entry> entries = new HashSet<Entry>();
    
    for (int b = 2; b < 101; ++b) {
      for (int e = 2; e < 101; ++e) {
        final Entry entry = new Entry(b, e);
        
        entries.add(entry);
      }
    }
    
    return entries.size();
  }
  
  @Test
  public void eyeballTest() {
    System.out.println(distinctPowers());
  }
  
  public static void main(String[] args) {
    JUnitCore.main("Solution");
  }
}