I've been studying a paper, and I recently tried discussing it with someone in person, and that made me realize I need some help with talking in math

How would you say the following in an efficient way (i.e. without having to explain it all the time, specially the index of summation)?

$\displaystyle \sum_{0<i_1<...<i_n<p} \left(\frac{i_1}{3}\right) \frac{(-1)^{i_1}}{i_1 i_2 \cdot \cdot \cdot i_n} $

where $\displaystyle \left(\frac{i_1}{3}\right)$ is the Legendre symbol, n is a positive odd integer and p is a prime such that p>n+1.

I'm not sure how I would say the summation part (the index) because it's not a straightforward from i=1 to p-1. It's a combination of unique (not equal) i's arranged in order, where 0<i<p.

Also, I'm not sure how to say the Legendre part ... would it be "the Legendre of i_1 over 3"?

Thanks, any help would be much appreciated