TITLE: How to prove $n$ is prime?
QUESTION [7 upvotes]: Let $n \gt 1$ and 
$$\left\lfloor\frac n 1\right\rfloor + \left\lfloor\frac n2\right\rfloor + \ldots + \left\lfloor\frac n n\right\rfloor = \left\lfloor\frac{n-1}{1}\right\rfloor + \left\lfloor\frac{n-1}{2}\right\rfloor + \ldots + \left\lfloor\frac{n-1}{n-1}\right\rfloor + 2$$ 
and $\lfloor \cdot \rfloor$ is the floor function. How to prove that $n$ is a prime?
Thanks in advance.

REPLY [3 votes]: i have a question if i define the function $ \sigma (x)= \sum_{n=1}^{x}d $ and 'd' is the function divisor isn't the problem $ \sigma(x)=\sigma(x-1)+2 $