A considerable repeated substring $t \leqslant s \in \Sigma^*$ is a string of length $2$ that occurs at least 3 times disjointly within $s$ or a string of length $3$ or more that occurs at least $2$ times disjointly within $s$.
So for $|\Sigma| = 1$, $s = a^n$ it's $|s| = 6$, since we have $(aa)(aa)(aa)$ or $(aaa)(aaa)$ but not less than 6, since you can't do the same for $n = 5, 4, 3, 2, 1$.
Thus it's going to be a function of alphabet size.
For $|\Sigma| = 2$. I'll work out the possibilities:
$$ aaaaabbbbbaba $$
So it's $|s| = 13$. Not too shabby. My strategy was to make the string as long as possible before switching chars.
What's the general estimate?
One more example: $|\Sigma| = 3$ $$ s = aaaaabbbbbcccccacbacabcba $$ which is probably not quite exact, since I'm not sure how I'm actually deciding, but $f(3) = |s| = 25$.