Consider the sequence \((a_k)_{k\ge 1}\) of positive rational numbers defined by \(a_1 = \frac{2020}{2021}\) and for \(k\ge 1\), if \(a_k = \frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\), then \[a_{k+1} = \frac{m + 18}{n+19}.\] Determine the sum of all positive integers \(j\) such that the rational number \(a_j\) can be written in the form \(\frac{t}{t+1}\) for some positive integer \(t \).