$U(n) =$ the smallest strictly positive integer $k$ such that $2^k-1$ is divisible by the first $n$ primes. What are the first values of $U(n)$?

Question

$U(n) =$ the smallest strictly positive integer $k$ such that $2^k-1$ is divisible by the first $n$ prime numbers (except for the first prime number: $2$).

What are the first values of $U(n)$ up to $n=11$ ?

I've already found the first values of $U(n)$ up to $n=4$ :

• $U(2) = 2$ $(4)$
• $U(3) = 4$ $(16)$
• $U(4) = 12$ $(4096)$