I have $2$ questions about notation.
Question 1.
Suppose, numbers are as follows.
$\left\{3\right\}\longrightarrow7$
$\left\{3,6\right\}\longrightarrow9$
$\left\{3,6,7\right\}\longrightarrow11$
$\left\{3,6,7,5\right\}\longrightarrow15$
$...............$
$\left\{p_1,p_2,p_3,...p_n\right\}\longrightarrow q_n$
And $p_1,p_2,...,p_{n}$ are arbitrary natural numbers.But, the value $q_n$ depend on the values of ${p_1,p_2,...,p_n}.$
I want to write a notation.
I think, I can write, for example,
$$f(p_1,p_2,...p_n)=q_n$$ like a function.Is it correct or ıs there an other notation?
Question 2.
Which notation is correct?
$\sum_{n=1}^{k} 2^{n}× n^2$ or $\sum_{n=1}^{k} (2^{n}× n^2)$
and
$\sum_{n=1}^{k} 2^{n}+n^2$ or $\sum_{n=1}^{k} (2^{n}+n^2)$