Integers not overtaken by m + τ(m)

Find n > 24 such that m + τ(m) ≤ n + 2 for every m < n, where τ counts divisors, or prove that 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/647",
14	"id": "647",
15	"curator": "Thomas Bloom",
16	"poser": "Paul Erdős and John Selfridge",
17	"status": "open, £25 prize",
18	"as_of": "2026-10-20",
19	"prize": "£25",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}