Imagine a number which has the property that the sum of all its divisors (including 1,
but excluding the number itself) equals the number. Such a number could be considered happy.
Now imagine a group of n numbers that are related in the following way: the sum
of the divisors of the first number (except the first number itself) is equal to the second
number, the sum of the divisors of the second number (except the second number itself)
is equal to the third number, and so on, and the sum of the divisors of the n
(except the n
th number itself) is equal to the first number. The numbers making up such
a set could be considered loopy.
Write a computer program to find loopy numbers under 9,000,000. How many loops
can you find? How big a loop can you find?
Relates to Objectives
1.1, 1.2, 1.3, 2.1, 2.2, 2.4, 2.7, 2.8, 3.1, 3.3, 3.5, 3.6, 4.1, 4.2, 4.3