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# Smallest inetger not divisible by integers in a finite set

Hello all, if $a_1,a_2, \ldots a_t$ are $t$ integers $\geq 2$, the set $G(a_1,a_2, \ldots a_t)=\lbrace N \geq 1 |$ In any sequence of $N$ consecutive integers there is at least one not divisible by any of $a_1,a_2, \ldots a_t\rbrace$ is nonempty (it contains $a_1a_2 \ldots a_t$) so it has a minimal element which we denote by $g(a_1,a_2, \ldots a_t)$.

Question 1 : Is there a uniform bound $\gamma (t)$, depending only on $t$, such that $\gamma (t) \geq g(a_1,a_2, \ldots a_t)$ for any $a_1,a_2, \ldots a_t$ ? For example, we may take $\gamma(2)=4$.

Question 2 : If $\gamma$ is well-defined, are any asymptotics known about $\gamma(t)$ ?