[math-fun] more groups than rings, surprise

The Dec 2020 issue of the Amer Math Monthly has an article Desmond MacHale, Are there more finite rings than finite groups?, Amer. Math. Monthly, 127:10 (2020), 936-938. showing that there are infinitely many n such that there are more groups with n elements than rings with n elements. He gives one example, n = 36355, and asks if this is the smallest such n. This is a sequence not yet in the OEIS! Anyone care to investigate? These are the n such that A000001(n) > A027623(n).