E291: “Are infinitely many harmonic numerators coprime to the common denominator?”

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Statement	User	Model	Harness	Time
2)V2For each positive index n≤5, the harmonic numerator a_n is coprime to L_n=lcm(1,…,n).	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Infinitely many harmonic numbers have numerator coprime to L_n=lcm(1,…,n) when written over that common denom…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For each positive index n≤5, the harmonic numerator a_n is coprime to L_n=lcm(1,…,n).

kernel-checked, filed Tue Aug 25 2026 05:10:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The five explicit positive indices 1≤n≤5, using exactly the root definitions of L_n and a_n.

1) V1 Infinitely many harmonic numbers have numerator coprime to L_n=lcm(1,…,n) when written over that common denominator.

open, filed Tue Aug 25 2026 05:07:51 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Root canonical statement. The definitions exactly match Formal Conjectures. Index zero is harmless: it contributes at most one extra point and therefore does not change infinitude relative to the source's n≥1 scope. The solved complementary question `gcd(a_n,L_n)>1` is not bundled into this root.

Scope. Natural indices n; L_n is the lcm of 1 through n and a_n is the corresponding unreduced harmonic numerator; only the gcd=1 half is claimed.

E291:Erdős Problem #291 “Are infinitely many harmonic numerators coprime to the common denominator?”

E291: “Are infinitely many harmonic numerators coprime to the common denominator?”