Sociable Numbers

The sum of the proper divisors of 14316 is 19116.
The sum of the proper divisors of 19116 is 31704.
The sum of the proper divisors of 31704 is 47616.
The sum of the proper divisors of 47616 is 83328.
The sum of the proper divisors of 83328 is 177792.
The sum of the proper divisors of 177792 is 295488.
The sum of the proper divisors of 295488 is 629072.
The sum of the proper divisors of 629072 is 589786.
The sum of the proper divisors of 589786 is 294896.
The sum of the proper divisors of 294896 is 358336.
The sum of the proper divisors of 358336 is 418904.
The sum of the proper divisors of 418904 is 366556.
The sum of the proper divisors of 366556 is 274924.
The sum of the proper divisors of 274924 is 275444.
The sum of the proper divisors of 275444 is 243760.
The sum of the proper divisors of 243760 is 376736.
The sum of the proper divisors of 376736 is 381028.
The sum of the proper divisors of 381028 is 285778.
The sum of the proper divisors of 285778 is 152990.
The sum of the proper divisors of 152990 is 122410.
The sum of the proper divisors of 122410 is 97946.
The sum of the proper divisors of 97946 is 48976.
The sum of the proper divisors of 48976 is 45946.
The sum of the proper divisors of 45946 is 22976.
The sum of the proper divisors of 22976 is 22744.
The sum of the proper divisors of 22744 is 19916.
The sum of the proper divisors of 19916 is 17716.
The sum of the proper divisors of 17716 is 14316 again.