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Odd weird numbers

Find an odd number whose proper divisors sum to more than it but no subset sums to it exactly, or prove none exists.

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1{
2 "domain": "mathematics",
3 "topics": [
4 "number-theory"
5 ],
6 "type": "construction",
7 "also": [
8 "proof"
9 ],
10 "source": {
11 "key": "erdos",
12 "name": "Erdős Problems",
13 "url": "https://www.erdosproblems.com/470",
14 "id": "470",
15 "curator": "Thomas Bloom",
16 "poser": "S. J. Benkoski and Paul Erdős",
17 "status": "open, $10 prize",
18 "as_of": "2026-10-20",
19 "prize": "$10",
20 "catalog": "0521c19bbd38"
21 }
22}