Conjecture that every odd abundant number is semiperfect

An integer $n$ is abundant if $\sigma(n)>2n$, and it is semiperfect if it equals the sum of some of its proper divisors. Odd-abundant semiperfectness conjecture. Every odd abundant number is semiperfect. This is equivalent to the assertion that no odd weird number exists; the paper notes that computations had ruled out odd weird numbers only up to $10^{21}$, so the general question remains open.