bibkey: ferreira2026a399232 authors: Rui Ferreira year: 2026 title: “OEIS A399232, odd-power residue sum and radical identity” doi: null url: https://raw.githubusercontent.com/oeis/oeisdata/2ce625d68f85e35e26e15c0d9681f69280c095e7/seq/A399/A399232.seq claim: “a(n) appears to satisfy rad(2n+1) = (2n+1)^2 / ((2*n+1)^2 - a(n)).” strata_touched:
- D5/S3/ArithSums/FerreiraOddPowerResidueRadical license: CC-BY-SA-4.0 triage: anchor
Ferreira’s odd-power residue sum
The OEIS A399232 NAME is:
a(n) = Sum_{k=1..4n+2} (k^(4n+1) mod (2*n+1)).
The first COMMENT is:
a(n) appears to satisfy rad(2n+1) = (2n+1)^2 / ((2*n+1)^2 - a(n)).
The OFFSET is 1,1. Thus the indices are all natural numbers n >= 1.
The remainder is the least nonnegative remainder, and rad(m) is the product
of the distinct prime divisors of m. The proposed quotient is rational;
its signed denominator must be strictly positive. The neighboring COMMENT
about numbers of the form x*(x-1) is outside this assertion.
Verified locator
https://raw.githubusercontent.com/oeis/oeisdata/2ce625d68f85e35e26e15c0d9681f69280c095e7/seq/A399/A399232.seq
The official OEIS export identifies revision 23, Sep 01 2026 11:39:12, and
the AUTHOR as _Rui Ferreira_, Aug 23 2026. The source has 984 bytes and
SHA-256 2d5409e351249e7e9d4853fea4ed5b8d0cce0c87c99dca1eab1de08cff080966.
The immutable source fetch returned HTTP 200.
Attribution and license
Source quotations and adapted source description are attributed to Rui Ferreira and the OEIS Foundation Inc. and distributed under CC BY-SA 4.0. The official license is the source license. The proof is a separate repository derivation; the source provides the assertion and sequence definition, not that proof.
Scope
The retained export and four available file-history revisions use tentative wording. Independent source observations include live OEIS HTTP 200 with the same COMMENT. A direct implementation-stage live request returned HTTP 403, so that request does not independently establish live status. Bounded OpenAlex, Math.SE, GitHub Lean-code, formal-conjectures and repository searches found no proof or refutation of the same assertion. This is a search-scope statement, with no claim of worldwide absence or historical priority.