# Bremen numbers

**Algebra**Level 4

For some values of the positive integer \(n\), there exists a polynomial in \(n\) variables whose image is exactly the set of the real positive numbers (note that 0 is not included in this set). The values of \(n\) verifying that property are called *Bremen numbers*.

Find the sum of all the *Bremen numbers* smaller than or equal to 30.

Submit 0 as your answer if you believe that there does not exist any *Bremen number* smaller than or equal to 30.