The number of divisors of $7!$ is

Let $f(x) = 2x^n + \lambda$,where $\lambda \in R$ and $n \in N$. Given $f(4) = 133$ and $f(5) = 255$,find the sum of all the positive integer divisors of $(f(3) - f(2))$.

If $2^{n}$ divides $16!$ and $2^{n+1}$ does not divide $16!$,then $n=$

If $p$ is a prime number,then $n^p - n$ is divisible by $p$ when $n$ is a

The number of divisors of $n = 38808$,excluding $1$ and $n$,is ....

The number of positive integers $n$ such that $n+3$ divides $n^3-3$ is