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100
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avatar+124 

How many numbers n less than 100 have exactly one divisor other than 1 and n?

 

How many positive integers less than 2000 are of the form x^n for some positive integer x and n\ge 2?

 

 

 

Thank you so much if you answered!wink

 Sep 17, 2019
 #1
avatar+104911 
+3

How many numbers n less than 100 have exactly one divisor other than 1 and n?

 

n     divsors

4       1   2   4

9       1   3   9

25     1   5  25

49     1   7  49

 

 

cool cool cool

 Sep 17, 2019
edited by CPhill  Sep 17, 2019
 #2
avatar+124 
+2

Thanks c-phil!

Imnotamaster  Sep 17, 2019
 #3
avatar+104911 
+1

That's the only ones I could think of  !!!!

 

 

 

cool cool cool

CPhill  Sep 17, 2019
 #4
avatar+2390 
+2

Notice Cphill's answers

 

they are ODD perfect squares except for 4, and ONLY prefect squares.

 

Answers like 81 won't work because it is a perfect power of 4 and 64 is a perfect cube.

 Sep 17, 2019
edited by CalculatorUser  Sep 17, 2019
 #5
avatar
-1

What is the value of n in your 2nd question? Is it 2 or > 2?

 Sep 17, 2019

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