// Calculate and print factors of successive Fibonacci numbers.
public class Primes
{
  public static void main (String[] args) {
   int f1 = 1, f2 = 2, n = 3;
   int f, f3, lim, nextdiv, divisor;
   boolean nodiv;
   while (n <= 45) {  // find factors of nth number
      System.out.print("n: " + n + "\t");
      System.out.print("F(n): " + f2 + " ");
      if (n < 40) System.out.print("\t");
      System.out.print("\tFactors: ");
      f = f2;
      while (f%2 == 0) { // check 2 as divisor
         f = f/2;
         System.out.print(2 + " ");
      }
      // all other divisors
      nextdiv = 3;
      while (f != 1) {
         // set lim > sqrt(f) 
         lim = 2;
         while (lim*lim < f)
            lim = lim*2;
         nodiv = true; // no divisors so far 
         divisor = nextdiv;
         while (nodiv && (divisor < lim)) {
            while (f%divisor == 0) {
               f = f/divisor;
               System.out.print(divisor + " ");
               nodiv = false;
            }
            divisor = divisor + 2;
         }
         nextdiv = divisor;
         if (nodiv) { // no divisor found 
            System.out.print(f);
            f = 1;
         }
      } // end "while (f != 1)"
      // move on to next number 
      System.out.println();
      n = n + 1;
      f3 = f1 + f2;
      f1 = f2;
      f2 = f3;
   } // end "while (n <= 40)"
  } // end of main
}

n: 3    F(n): 2                 Factors: 2 
n: 4    F(n): 3                 Factors: 3
n: 5    F(n): 5                 Factors: 5
n: 6    F(n): 8                 Factors: 2 2 2 
n: 7    F(n): 13                Factors: 13
n: 8    F(n): 21                Factors: 3 7
n: 9    F(n): 34                Factors: 2 17
n: 10   F(n): 55                Factors: 5 11
n: 11   F(n): 89                Factors: 89
n: 12   F(n): 144               Factors: 2 2 2 2 3 3 
n: 13   F(n): 233               Factors: 233
n: 14   F(n): 377               Factors: 13 29
n: 15   F(n): 610               Factors: 2 5 61
n: 16   F(n): 987               Factors: 3 7 47
n: 17   F(n): 1597              Factors: 1597
n: 18   F(n): 2584              Factors: 2 2 2 17 19
n: 19   F(n): 4181              Factors: 37 113
n: 20   F(n): 6765              Factors: 3 5 11 41
n: 21   F(n): 10946             Factors: 2 13 421
n: 22   F(n): 17711             Factors: 89 199
n: 23   F(n): 28657             Factors: 28657
n: 24   F(n): 46368             Factors: 2 2 2 2 2 3 3 7 23
n: 25   F(n): 75025             Factors: 5 5 3001
n: 26   F(n): 121393            Factors: 233 521
n: 27   F(n): 196418            Factors: 2 17 53 109
n: 28   F(n): 317811            Factors: 3 13 29 281
n: 29   F(n): 514229            Factors: 514229
n: 30   F(n): 832040            Factors: 2 2 2 5 11 31 61
n: 31   F(n): 1346269           Factors: 557 2417
n: 32   F(n): 2178309           Factors: 3 7 47 2207
n: 33   F(n): 3524578           Factors: 2 89 19801
n: 34   F(n): 5702887           Factors: 1597 3571
n: 35   F(n): 9227465           Factors: 5 13 141961
n: 36   F(n): 14930352          Factors: 2 2 2 2 3 3 3 17 19 107
n: 37   F(n): 24157817          Factors: 73 149 2221
n: 38   F(n): 39088169          Factors: 37 113 9349
n: 39   F(n): 63245986          Factors: 2 233 135721
n: 40   F(n): 102334155         Factors: 3 5 7 11 41 2161
n: 41   F(n): 165580141         Factors: 2789 59369
n: 42   F(n): 267914296         Factors: 2 2 2 13 29 211 421
n: 43   F(n): 433494437         Factors: 433494437
n: 44   F(n): 701408733         Factors: 3 43 89 199 307
n: 45   F(n): 1134903170        Factors: 2 5 17 61 109441