Enumerating the Boolean functions satisfying one or several cryptographic criteria is useful. However, for a given number of variables, the number of Boolean functions with maximum AI is not known, either the previous known bound on the number is not good. In this paper, we investigate the enumeration of Boolean functions with maximum AI. First, we improve the lower bound on the number of even-variable Boolean functions with maximum AI, our new lower bound is better than the previous lower bounds. Then, for the first time, a significant lower bound on the number of 1-resilient Boolean functions with maximum AI is provided.