Erdős Problem 825: formalise necessary_cond variant

Opening an issue for [Erdős Problem #825](https://www.erdosproblems.com/825), specifically the erdos_825.variants.necessary_cond theorem in FormalConjectures/ErdosProblems/825.lean.

The file is already tagged @[category research solved]. The underlying mathematical result (Larsen's theorem) has already been accepted, so this is not a new mathematical claim. What is outstanding is that the Lean formalisation of the necessary_cond variant is still shown as _sorry._ This issue is to track closing that formalisation gap.

For context before I open the PR: the approach uses n=70 as a witness. 70 is a "weird number", abundant (σ(70)=144>140) but with no subset of its proper divisors summing to 70. That's enough to force C>2.

For full disclosure (and the same as I will note in the PR) this was done with AI assistance. Claude handled orchestration, codex/GPT-5.6 wrote the Lean tactics, and the compiler was the check at every step. I have reviewed the resulting proof myself and independently re-verified it.

PR to follow once this issue exists.

Open FormalConjectures/ErdosProblems/825.lean and inspect erdos_825.variants.necessary_cond alongside the related variants. Use the n=70 weird-number witness and the existing Larsen's theorem context, then verify the Lean file compiles with the necessary_cond statement no longer marked sorry.

Written by the indexing model from the issue text.