Question 91
For a positive integer $n$, let $S(n)$ be the sum of all those integers $k$, $1 \le k \le n$, which are relatively prime to $n$ (i.e., the greatest common divisor of $k$ and $n$ is $1$).
(1) Find the value of $S(30)$ (you don't need to give a proof).
(2) Determine all $n$ for which $S(n)$ is a prime.
Here, by a prime we mean an integer greater than or equal to $2$, which has no factor other than $1$ and itself.
(1) Find the value of $S(30)$ (you don't need to give a proof).
(2) Determine all $n$ for which $S(n)$ is a prime.
Here, by a prime we mean an integer greater than or equal to $2$, which has no factor other than $1$ and itself.