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Call a positive integer kinda-prime if it has a prime number of positive integer divisors. If there are 168 prime numbers less than 1000, how many kinda-prime positive integers are there less than 1000?

 Apr 11, 2021
 #1
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https://web2.0calc.com/questions/help-with-permutations_1

 

It's answered already. :)))

 

=^._.^=

 Apr 11, 2021
 #2
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i didnt understand it

Guest Apr 11, 2021
 #3
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Hmm, I shall try my best to solve. :))

So, we need our numbers to be in the form of a^b where a is a prime number, and b is one less than a prime number. 

If a = 2, then b can be 1, 2, 4, 6. (4 options)

If a = 3, then b can be 1, 2, 4, 6. (4 options)

If a = 5, then b can be 1, 2, 4. (3 options)

If a = 7, then b can be 1, 2. (2 optinos)

If a = 11, then be can be 1, 2. (2 options)

From there, any a from 11 - 31 will have 2 options for b (1, 2). 

4+4+3+21*2 = 53. 

 

Someone please check this, I'm really not confident, but I hope this helped.

 

=^._.^=

catmg  Apr 11, 2021

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