+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 \(2 \le n \le 50\)?
+129840 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 ≤ n ≤ 50?
I think I understand this one.........
All the n"s ≥ 2 and ≤ 25 will divide at least one n from 2 to 50 inclusive...so each of these will divide g(n)
And all the composite n's > 25 but ≤ 50 can be divided by at least two n's from 2 to 25 inclusive
But the primes from 25 to 50 cannot be formed by any other factors than 1 and themselves
Thus, the "n"s" that will not divide g(n) will be all the primes > 25 and < 50
And these are 29, 31, 37, 41, 43, 47
+129840 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 ≤ n ≤ 50?
I think I understand this one.........
All the n"s ≥ 2 and ≤ 25 will divide at least one n from 2 to 50 inclusive...so each of these will divide g(n)
And all the composite n's > 25 but ≤ 50 can be divided by at least two n's from 2 to 25 inclusive
But the primes from 25 to 50 cannot be formed by any other factors than 1 and themselves
Thus, the "n"s" that will not divide g(n) will be all the primes > 25 and < 50
And these are 29, 31, 37, 41, 43, 47
