What is the sum of all factors of 45000 which are divisible by 10
That would be 10 times the sum of all the factors of 4500. The sum-of-factors function has the following property: if where the are distinct primes, then
Thus So the answer to the problem is 141960.
I don’t see anything wrong with the proof, particularly the formula
Shall we prove this formula? Then perhaps you’ll feel less afraid of using it.
First, we prove that if then Note that a divisor of can be written as where and and Hence
Next, not that if is a prime and a positive integer,
Combining the two results established above gives the required formula for the sum-of-factors function