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erdős #250

← #249 · #251 → (packet.json; erdosproblems.com)

Is $\sum \frac{σ ( n )}{2 ^{n}}$ irrational? (Here $σ (n)$ is the sum of divisors function.)

Worked, still open.

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

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · solved (literature)

theorem erdos_250  : (∀ x, HasSum (fun (n : ℕ) => σ 1 n / (2 : ℝ) ^ n) x → Irrational x) ↔
    answer(True)

formal-conjectures/250.lean ↗

oeis

A066766 — Decimal expansion of Sum_{k>=1} sigma(k)/2^k where sigma(k) is the sum of divisors of k, 1 <= d <= k.2,7,4,4,0,3,3,8,8,8,7,5,9,4,8,8,3,6,0,4,8,0,2,1,4,8,9,1,4,9,2,2,7,2,1,6,4,3,1,1,4,2,8,9,8,1,3,1,9,6,3,9,3,1,7,8,4,8,5,2,

links

Google DeepMind Formal Conjectures project · link

status

solved

finding.noted · reviewer:will-blair · 1 day

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