Is $n \sum \frac{ϕ ( n )}{2 ^{n}}$ irrational? Here $ϕ$ is the Euler totient function.

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

[ S=\sum_{n=1}^{\infty}\frac{\varphi(n)}{2^{n}} . ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_249 : answer(sorry) ↔ Irrational (∑' n : ℕ, (φ n) / (2 ^ n))

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