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number theory intermediate
Problem
An is a positive integer, the sum of whose distinct proper factors is greater than the number. (The of a number are all of its factors except the number itself.) How many numbers less than 25 are abundant numbers?
Solution
First we note that no prime number is abundant since the sum of the proper factors of any prime is 1. Analyzing the remaining numbers, we find that 12 (), 18 (), 20 (), and 24 () are abundant numbers. Thus, numbers less than 25 are abundant numbers.
Final answer
4