6. We use $S_{k}$ to denote an arithmetic sequence with the first term $k$ and a common difference of $k^{2}$, for example, $S_{3}$ is $3, 12, 21, \cdots$. If 306 is a term in $S_{k}$, the sum of all $k$ that satisfy this condition is $\qquad$.
【Answer】 326
【Solution】Since the first term of $S_{k}$ is $k$, and the common difference is $k^{2}$, a certain term in it can be expressed as $k+m k^{2}=k(1+m k)$. If 306 is a term in $S_{k}$, then $k(1+m k)=306 \Rightarrow k \mid 306$. Since $306=2 \times 3^{2} \times 17$, the satisfying $k=1, 2, 17, 306$ (note that when $k \neq 306$, $k<1+m k$; when $k=306$, $m=0$), so the sum of these numbers is $1+2+17+306=326$