MathDB

18

Part of 2015 AMC 12/AHSME

Problems(1)

Sum of prime factors, not necessarily distinct

Source: 2015 AMC 12B Problem 18

2/26/2015
For every composite positive integer nn, define r(n)r(n) to be the sum of the factors in the prime factorization of nn. For example, r(50)=12r(50)=12 because the prime factorization of 5050 is 2⋅52 2 \cdot 5^2 , and 2+5+5=12 2 + 5 + 5 = 12 . What is the range of the function rr, {r(n):n is a composite positive integer} \{ r(n) : n \ \text{is a composite positive integer} \} ?
(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 3 (E) the set of integers greater than 4
functionnumber theoryprime factorizationAMC