import java.util.ArrayList;
import java.util.List;
import java.util.Set;
import java.util.TreeSet;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public final class AchlllesNumbers {

	public static void main(String[] aArgs) {
		Set<Integer> perfectPowers = perfectPowers(500_000);
	    List<Integer> achilles = achilles(1, 250_000, perfectPowers);
	    List<Integer> totients = totients(250_000);

	    System.out.println("First 50 Achilles numbers:");
	    for ( int i = 0; i < 50; i++ ) {
	    	System.out.print(String.format("%4d%s", achilles.get(i), ( ( i + 1 ) % 10 == 0 ) ? "\n" : " "));
	    }
	    System.out.println();
	
	    System.out.println("First 50 strong Achilles numbers:");
	    for ( int i = 0, count = 0; count < 50; i++ ) {
	    	if ( achilles.contains(totients.get(achilles.get(i))) ) {
	    		System.out.print(String.format("%6d%s", achilles.get(i), ( ++count % 10 == 0 ) ? "\n" : " "));
	    	}
	    }
	    System.out.println();
	
	    System.out.println("Number of Achilles numbers with:");
	    for ( int i = 100; i < 1_000_000; i *= 10 ) {
	    	final int digits = String.valueOf(i).length() - 1;
	    	System.out.println("    " + digits + " digits: " + achilles(i / 10, i - 1, perfectPowers).size());
	    }
	}
	
	private static List<Integer> achilles(int aFrom, int aTo, Set<Integer> aPerfectPowers) {
	    Set<Integer> result = new TreeSet<Integer>();
	    final int cubeRoot = (int) Math.cbrt(aTo / 4);
	    final int squareRoot = (int) Math.sqrt(aTo / 8);
	    for ( int b = 2; b <= cubeRoot; b++ ) {
	        final int bCubed = b * b * b;
	        for ( int a = 2; a <= squareRoot; a++ ) {
	            int achilles = bCubed * a * a;
	            if ( achilles >= aTo ) {
	                break;
	            }
	            if ( achilles >= aFrom && ! aPerfectPowers.contains(achilles) ) {
	                result.add(achilles);
	            }
	        }
	    }
	    return new ArrayList<Integer>(result);
	}
	
	private static Set<Integer> perfectPowers(int aN) {
	    Set<Integer> result = new TreeSet<Integer>();
	    for ( int i = 2, root = (int) Math.sqrt(aN); i <= root; i++ ) {
	        for ( int perfect = i * i; perfect < aN; perfect *= i ) {
	            result.add(perfect);
	        }
	    }
	    return result;
	}
	
	private static List<Integer> totients(int aN) {
		List<Integer> result = IntStream.rangeClosed(0, aN).boxed().collect(Collectors.toList());;
		for ( int i = 2; i <= aN; i++ ) {
			if ( result.get(i) == i ) {
				result.set(i, i - 1);
				for ( int j = i * 2; j <= aN; j = j + i ) {
					result.set(j, ( result.get(j) / i ) * ( i - 1 ));
				}
			}
		}
		return result;
	}	

}