Erdős Problem #470 — An integer $n$ has been called weird [Ben-Er (74)] if $\frac{\sigma(n)}{n} \geqslant 2$ and $n \neq d_1 + ... + d_k$ where the $d_i$ are distinct proper divisors of $n$.

An integer $n$ has been called weird [Ben-Er (74)] if $\frac{\sigma(n)}{n} \geqslant 2$ and $n \neq d_1 + ... + d_k$ where the $d_i$ are distinct proper divisors of $n$. Are there any odd weird numbers? Are there infinitely many primitive weird numbers, i.e., so that no proper divisor of $n$ is weird?