erdős #252
Let and . Isirrational?
Worked, still open.
number theory · open · formalized (Lean) · 0 attempts
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vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Write [ \alpha_k =\sum_{n=1}^{\infty}\frac{\sigma_k(n)}{n!},\qquad \sigma_k(n)=\sum_{d\mid n} d^k . ]
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
2 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_252 :
answer(sorry) ↔ ∀ k ≥ 1, Irrational (erdos_252_sum k)formal-conjectures/252.lean ↗oeis
A227988 — Decimal expansion of Sum_{n >= 1} sigma_1(n)/n!.3,5,2,7,0,0,0,4,7,1,8,5,2,9,5,2,8,2,9,7,6,1,5,3,6,7,9,1,7,6,9,3,2,6,2,0,3,7,6,3,5,6,4,3,4,4,9,5,2,4,0,8,2,7,7,6,0,5,7,1,A227989 — Decimal expansion of Sum_{n >= 1} sigma_2(n)/n!.6,3,4,0,0,9,6,6,6,8,8,9,2,1,7,1,6,3,8,8,2,9,9,6,5,9,9,4,0,0,7,5,0,4,6,0,7,8,6,3,6,4,4,3,3,5,5,9,8,9,0,1,7,8,5,4,3,9,9,6,
status
open