The Ionof (Integer on number of factors) of an integer is the integer divided by the number of factors it has.?

Posted on 2016-05-17 18:52:00 in Math by AWMS

The Ionof (Integer on number of factors) of an integer is the integer divided by the number of factors it has. For example, 18 has 6 factors so Ionof (18)=18/6= 3 and 27 has 4 factors so Ionof(27) =27/4 =6.75 

a) Find Ionof(36) 

b) Explain why Ionof(pq) is not an integer if p and q are distinct primes. 

c) If p and q are distinct primes, find all numbers of the form (pq)4 whose Ionof is an integer. 

d) Show that the square of any prime number is the Ionof of some integer

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