Difference between revisions of "2013 AMC 10B Problems/Problem 24"
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==Problem== | ==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</math>) such that the sum of the four divisors is equal to <math>n</math>. How many numbers in the set <math>\{ 2010,2011,2012, \ | + | 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</math>) such that the sum of the four divisors is equal to <math>n</math>. How many numbers in the set <math>\{ 2010,2011,2012,\dotsc,2019 \}</math> are nice? |
<math> \textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5</math> | <math> \textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5</math> | ||
==Solution== | ==Solution== | ||
Revision as of 16:13, 21 February 2013
Problem
A positive integer 
is nice if there is a positive integer 
with exactly four positive divisors (including 
and ) such that the sum of the four divisors is equal to . How many numbers in the set 
are nice?
