Show a Java class called CyclicSequence:

The solution to this question must NOT use arrays or ArrayLists.

The class should output numbers whose sum of proper divisors form a cyclic sequence that begins and ends with the same number.

Include a method called generateSequence that takes a number as a parameter and outputs the other numbers in the sequence. You can use any number in the list shown below as the starting point to generate the rest of the values in that cyclic sequence.

You can also include a method called sumProperDivisors to calculate the sum of all the number's proper divisors and call it from the generateSequence method.

The output must print the numbers int the sequence (after each value is calculated) separated by 2 spaces.

Use the following to test you logic:

• The numbers that result in a 2-cycle sequence:  220, 284
• The numbers result in a 4-cycle sequence: 1547860, 1727636, 1305184, 1264460
• The numbers result in a 5-cycle sequence: 12496, 14288, 15472, 14536, 14264
• The only known numbers that result in a 28-cycle sequence are: 14316, 19116, 31704, 47616, 83328,
  177792, 295488, 629072, 589786, 294896, 358336, 418904, 366556, 274924, 275444, 243760, 376736,
  381028, 285778, 152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916, 17716.
• All other numbers will result in an infinite loop. Your logic will only need to work for the numbers listed above.

 

Example:

Start with  

1547860: the sum of all its proper divisors is 1727636. 

1727636: the sum of all its proper divisors is 1305184

1305184: the sum of all its proper divisors is 1264460

1264460: the sum of all its proper divisors is 1547860