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Difference between revisions of "2015 AMC 12B Problems/Problem 18"

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For every composite positive integer <math>n</math>, define <math>r(n)</math> to be the sum of the factors in the prime factorization of <math>n</math>. For example, <math>r(50) = 12</math> because the prime factorization of <math>50</math> is <math>2 \times 5^{2}</math>, and <math>2 + 5 + 5 = 12</math>. What is the range of the function <math>r</math>, <math>\{r(n): n \text{ is a composite positive integer}\}</math> ?
 
For every composite positive integer <math>n</math>, define <math>r(n)</math> to be the sum of the factors in the prime factorization of <math>n</math>. For example, <math>r(50) = 12</math> because the prime factorization of <math>50</math> is <math>2 \times 5^{2}</math>, and <math>2 + 5 + 5 = 12</math>. What is the range of the function <math>r</math>, <math>\{r(n): n \text{ is a composite positive integer}\}</math> ?
  
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<math>\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?</math>
+
<math>\textbf{(A)}\; \text{the set of positive integers} \\
 +
\textbf{(B)}\; \text{the set of composite positive integers} \\
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\textbf{(C)}\; \text{the set of even positive integers} \\
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\textbf{(D)}\; \text{the set of integers greater than 3} \\
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\textbf{(E)}\; \text{the set of integers greater than 4}</math>
  
 
==Solution==
 
==Solution==

Revision as of 23:19, 3 March 2015

Problem

For every composite positive integer $n$, define $r(n)$ to be the sum of the factors in the prime factorization of $n$. For example, $r(50) = 12$ because the prime factorization of $50$ is $2 \times 5^{2}$, and $2 + 5 + 5 = 12$. What is the range of the function $r$, $\{r(n): n \text{ is a composite positive integer}\}$ ?

$\textbf{(A)}\; \text{the set of positive integers} \\ \textbf{(B)}\; \text{the set of composite positive integers} \\ \textbf{(C)}\; \text{the set of even positive integers} \\ \textbf{(D)}\; \text{the set of integers greater than 3} \\ \textbf{(E)}\; \text{the set of integers greater than 4}$

Solution

See Also

2015 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 17 		Followed by
Problem 19
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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