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How many of the numbers from the set \(\{1,\ 2,\ 3,\ldots,\ 50\} \) have a perfect square factor other than one?

 Oct 6, 2018
 #1
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+1

These are the ones I can think of:

 

(8, 12, 16, 18, 20, 24, 27, 28, 32, 36, 40, 44, 45, 48, 50)=15

 Oct 7, 2018
 #2
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+2

Rom has interpreted the question a bit differently from me. :)

 

All the multiples of 4 

4,8,12,16,20,24,28,32,36,40,44,48

 

All the multiples of 9 that you do not already have

9,18,27, not36, 45

 

you already have all the multiples of 16

 

All the multiples of 25

25, 50

 

you already have all the multiples of 36

 

All the multiples of 49

 

so that is 

 

4, 8, 9, 12,16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50    So I count 19 of them.

 Oct 7, 2018

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