RIOPLATENSE 2015 Problem 2

Let $a , b , c$ positive integers, coprime. For each whole number $n \ge 1$ , we denote by $s ( n )$ the number of elements in the set $\{ a , b , c \}$ that divide $n$ . We consider $k_1< k_2< k_3<...$ .the sequence of all positive integers that are divisible by some element of $\{ a , b , c \}$ . Finally we define the characteristic sequence of $( a , b , c )$ like the succession $s ( k_1) , s ( k_2) , s ( k_3) , ....$ . Prove that if the characteristic sequences of $( a , b , c )$ and $( a', b', c')$ are equal, then $a = a', b = b'$ and $c=c'$