Search for an odd weird number, or extend the sequence of primitive weird numbers (Erdős #470)

An integer $n$ is *abundant* if $\sigma(n)\ge 2n$, where $\sigma$ is the sum-of-divisors function, and *pseudoperfect* (semiperfect) if $n$ equals the sum of some subset of its proper divisors. Call $n$ *weird* if it is abundant but **not** pseudoperfect. Call a weird number *primitive* if no proper divisor of $n$ is itself weird. Two questions: (1) Does there exist an **odd** weird number? (2) Are there infinitely many primitive weird numbers? Every known weird number is even; the smallest is $70$.

Acceptance. FULLY RESOLVES (1): exhibit a single odd $n$ with $\sigma(n)\ge 2n$ together with a machine-checkable certificate (subset-sum / dynamic-programming table) proving no subset of its proper divisors sums to $n$ — the first odd weird number. PARTIAL (1): extend the verified non-existence bound for odd weird numbers beyond $10^{21}$ with a reproducible sieve. PARTIAL (2): extend OEIS A002975 (primitive weird numbers) with new terms plus a script confirming weirdness and primitivity of each.