Is it true that for every sufficiently large positive integer n, one can always find at most [π(n)/2] integers, $a_1$, $a_2$, $a_3$, $a_3$, ... $a_{ [π(n)/2]}$, between 1 and n, such that each of the π(n) primes not greater that n divides at least one of the integers $a_1$, $a_1$+1, $a_2$, $a_2$+1, $a_3$, $a_3$ + 1, ..., $a_{[π(n)/2]}$, $a_{[π(n)/2]}$+1?

Is it true that for every sufficiently large positive integer $n$, one can always find at most $k=\lfloor\pi(n)/2\rfloor$ integers, $a_1,a_2,a_3,a_3,\dots a_k$, between $1$ and $n$, such that each of the $\pi(n)$ primes not greater that $n$ divides at least one of the integers $a_1,a_1+1,a_2,a_2+1,a_3,a_3+1,\dots,a_k,a_k+1$?

Is it true that for every sufficiently large positive integer n, one can always find at most [π(n)/2] integers $a_1$, $a_2$, $a_3$, $a_3$, ... $a_{ [π(n)/2]}$, such that each of the π(n) primes not greater that n divides at least one of the integers $a_1$, $a_1$+1, $a_2$, $a_2$+1, $a_3$, $a_3$ + 1, ..., $a_{[π(n)/2]}$, $a_{[π(n)/2]}$+1?

Is it true that for every sufficiently large positive integer n, one can always find at most [π(n)/2] integers, $a_1$, $a_2$, $a_3$, $a_3$, ... $a_{ [π(n)/2]}$, between 1 and n, such that each of the π(n) primes not greater that n divides at least one of the integers $a_1$, $a_1$+1, $a_2$, $a_2$+1, $a_3$, $a_3$ + 1, ..., $a_{[π(n)/2]}$, $a_{[π(n)/2]}$+1?