+48 Let g(n) be the product of the proper positive integer divisors of n. (Recall that a proper divisor of n is a divisor other than n.) For how many values of n does n not divide g(n), given that \(2 \le n \le 50\)?
+9665 \(\text{The question means:}\\ \text{How many values give } \dfrac{n}{g(n)}\text{ is not an integer?}\)
n=2, g(n)= 1 , 2/1 is an integer
n=3, g(n)= 1, 3/1 is an integer.
Looks like prime numbers does give n/g(n) = (some integer.)
Prime numbers between 2 and 50:
2, 3, 5, 7 , 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Total 15 numbers.
also n = 6 does give n/g(n) = integer.
Total 16 numbers now.
Answer = (Number of integers between 2 and 50) - 16
= 50 - 2 + 1 - 16
= 33
33 values of n does n not divide g(n).
Finish!!
