CMIMC 2021 Algebra and Number Theory Division 2 Problem 7

Past Contests CMIMC CMIMC - 2021 Algebra and Number Theory D2
1

For each positive integer n, let \sigma(n) denote the sum of the positive integer divisors of n. How many positive integers n \leq 2021 satisfy

\sigma(3 n) \geq \sigma(n)+\sigma(2 n) ?