$a_n = 100+n^2$

The numbers in the sequence $101, 104, 109,116, . . .$ are of the form $a_n = 100+n^2$ , where $n = 1, 2, 3, . . . .$ For each $n$ , let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$ .

Find the maximum value of $d_n$ as $n$ ranges through the positive integers.