A set $X=\{ x_1,x_2,\ldots,x_n \}$ consisting of $n$ positive integers is given. It is known that the greatest common divisor of any four different elements of $X$ is $1$. For every number $x_i$ let $m_i$ be the number of elements of $X$, which are divisible by $x_i$ For every $n \geq 4$, find the maximal possible value of the sum $m_1+\ldots+m_n$ A. Vaidzelevich