## Task 1 - 250731

Determine for each natural number $n>0$ the number of those natural numbers that are divisors of the number $2 n$!
For every natural number $n>0$:

A natural number greater than 1 is a divisor of $2 n$ if and only if its prime factorization contains no other prime factors than the prime number 2, and no more than $n$ such factors. This applies precisely to the $n$ natural numbers

$$
21,22, \ldots, 2 n-1,2 n
$$

Furthermore, 1 is a divisor of the number $2 n$. (2)

The total number of all natural numbers listed in (1) and (2) that are divisors of $2 n$ is therefore $n+1$.