Sun's characterization conjecture for primitive covering numbers

Let $L$ be a primitive covering number, meaning a positive integer that is a covering number but has no proper divisor that is a covering number. Write its prime factorization as

$$L=p_1^{a_1}\cdots p_r^{a_r},$$

where $p_1,\ldots,p_r$ are distinct primes and $a_1,\ldots,a_r$ are positive integers. Sun's conjecture. Every primitive covering number can be written in this form with the primes and exponents satisfying the condition given in equation (Eq:Sun) of the source. The conjecture proposed a characterization of all primitive covering numbers; the paper states that it is false and provides infinitely many counterexamples.