23. Given the set $X = \{ 1,2,3 \} , Y _ { n } = \{ 1,2,3 , m , n \} \left( n \in N ^ { * } \right)$, let\\
$S _ { n } = \left\{ ( a , b ) \mid a \text{ divides } b \text{ or } b \text{ divides } a , a \in X , b \in Y _ { n } \right\}$, and let $f ( n )$ denote the number of elements in set $S _ { n }$.\\
(1) Write out the value of $f ( 6 )$;\\
(2) When $n \geq 6$, write out the expression for $f ( n )$ and prove it using mathematical induction.