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erdős #259

← #258 · #260 → (packet.json; erdosproblems.com)

Is the sum $n \sum μ (n)^{2} \frac{n}{2 ^{n}}$ irrational?

Worked, still open.

irrationality · 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_259 : Irrational (∑' n : ℕ, (μ n) ^ 2 * n / (2 ^ n))

formal-conjectures/259.lean ↗

oeis

A371134 — Decimal expansion of Sum_{squarefree k>=1} k / 2^k.1,6,9,7,9,0,7,8,1,9,7,7,9,6,2,5,0,6,4,4,6,4,2,4,0,8,9,9,6,5,3,4,7,8,9,1,8,4,3,6,3,5,1,5,3,1,8,8,6,2,4,7,2,6,3,4,0,6,9,9,

status

solved

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

renders the record as of vev_d199cb2e · 1,338 events · hub