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2013 AMC 10B Problems/Problem 24

Revision as of 16:00, 21 February 2013 by Gengkev (talk | contribs) (Created page with "==Problem== A positive integer <math>n</math> is ''nice'' if there is a positive integer <math>m</math> with exactly four positive divisors (including <math>1</math> and <math>m...")
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Problem

A positive integer $n$ is nice if there is a positive integer $m$ with exactly four positive divisors (including $1$ and $m$) such that the sum of the four divisors is equal to $n$. How many numbers in the set $\{ 2010,2011,2012, \dots ,2019 \}$ are nice?

$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5$

Solution

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