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

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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