7. (10 points) 2016 students line up in a row, and from left to right, they report numbers $1, 2, \cdots, n$ $(n \geqslant 2)$. If the 2016th student reports the number $n$, then all students who report $n$ in this round will receive a New Year's gift. No matter what value $n$ takes, there will be
students who will not receive the New Year's gift.
576
【Solution】Solution: First, number the 2016 students from left to right as 1 - 2016. If a student reports a number $n$, it means that the student's number is exactly a multiple of $n$, so the students who are multiples of $n$ are all multiples of $n$, then $n$ must be divisible by 2016. Factorizing 2016 into prime factors gives $2016=2^{5} \times 3^{2} \times 7$. Therefore, numbers that are coprime with 2016 will never receive a gift.
The number of coprime numbers is $2016 \times\left(1-\frac{1}{2}\right) \times\left(1-\frac{1}{3}\right) \times\left(1-\frac{1}{7}\right)=576$ (numbers).
Therefore, the answer is: 576.