Three Does Not Divide

A classic use of the prefix function: to find the shortest string t such that s is t repeated a whole number of times, compute k = n - pi[n-1]. If k divides n, the answer is k, otherwise the answer is n.

For s = "abcabcab" the prefix function is

i     : 0 1 2 3 4 5 6 7
s[i]  : a b c a b c a b
pi[i] : 0 0 0 1 2 3 4 5

What is the length of the shortest t?