Problem:
For every composite positive integer , define to be the sum of the factors in the prime factorization of . For example, because the prime factorization of is , and . What is the range of the function ?
Answer Choices:
A. the set of positive integers
B. the set of composite positive integers
C. the set of even positive integers
D. the set of integers greater than
E. the set of integers greater than
Solution:
To be composite, a number must have at least two prime factors, and the smallest prime number is 2 . Therefore the smallest element in the range of is . To see that all integers greater than are in the range, note that for all , and for all .
The problems on this page are the property of the MAA's American Mathematics Competitions