KöMaL 2019 B5021

A positive integer $n$ is not divisible by 3. The sum of its positive divisors that leave a remainder of 1 when divided by 3 is $A(n)$, and the sum of its positive divisors that leave a remainder of 2 when divided by 3 is $B(n)$. Find those numbers $n$ for which $\big|A(n)-B(n)\big|<\sqrt{n}\,$.