Corpus.OEIS1157.conjecture
Conjecture: For each k = 2,3,..., all the rational numbers $\frac{\sigma_k(n)}{n^k} = \sum_{d|n} \frac{1}{d^k}$ (n = 1,2,3,...) have pairwise distinct fractional parts.
Sum of squares of divisors of
formal-conjectures · oeis · ams-11
Conjecture: For each k = 2,3,..., all the rational numbers
$\frac{\sigma_k(n)}{n^k} = \sum_{d|n} \frac{1}{d^k}$ (n = 1,2,3,...) have pairwise distinct
fractional parts. - Zhi-Wei Sun, Oct 15 2015
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A001157
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/1157.lean
Local target: Corpus.OEIS1157.conjecture
Source SHA-256: 1744b3fbf90353dd6274a2142a3cf9d280d64b7a131d327cf70c4f983b0103f1
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
Formal targets
Reusable lemmas
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Public discussion
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