Inspired by this fantastic numberphile video with Ben Sparks we are explored sequences of aliquot sums. An aliquot sum is the sum of proper factors of numbers.
The number 15 has factors 1, 3, 5, 15 but the proper factors don’t include the number itself so 15 has proper factors 1, 3, 5. Adding these together gives an aliqout sum of 1+3+5 = 8.
Now we find the aliquot sum of 8, which is 1+2+4 = 7. Then find the aliquot sum of 7, which is just 1 as 7 is a prime number. If we get to 1 we stop.
So 15 – 8 – 7 – 1.
Try with different starting numbers, do all numbers go to 1?
Aliquot 1 – Program to find the aliquot sum of a number
Aliquot 2 – Program to find the aliquot sequence of a starting number