bibkey: yanev2017a023887 authors: Olivier Gérard; Velin Yanev year: 2017 title: “OEIS A023887, sigma_n(n), with Yanev’s sigma_m identity” doi: null url: https://oeis.org/A023887 claim: “%N a(n) = sigma_n(n): sum of n-th powers of divisors of n. %F Conjecture: sigma_m(n) = sigma(n^m * rad(n)^(m-1))/sigma(rad(n)^(m-1)) for n > 0 and m > 0, where sigma = A000203 and rad = A007947. - Velin Yanev, Aug 24 2017” strata_touched:

• D5/S3/Arith/YanevSigmaRadicalIdentity license: citation-only triage: anchor

OEIS A023887 and Yanev’s divisor-power identity

A023887 is the sequence of diagonal divisor-power sums. Yanev’s formula relates the general sum sigma_m(n) to ordinary divisor sums and the radical for every positive natural n and m. The formal statement is its multiplied-out identity; both sides and the quotient’s denominator are positive. The year 2017 records the date of Yanev’s conjecture, while the AUTHOR line credits Olivier Gérard.

Sela Fried’s 2025 Theorem 3 in “Proofs of some conjectures of Yanev” (OEIS a006519.pdf) proves the m = 2 case on A001157. The general-m statement in A023887 is the claim addressed by this note’s formal reference.

Verified locator

The following source text and locator were supplied by the orchestrator on 2026-09-15; no online retrieval was performed by this implementation seat.

• URL: https://oeis.org/A023887
• %N (verbatim): a(n) = sigma_n(n): sum of n-th powers of divisors of n.
• %F (verbatim): Conjecture: sigma_m(n) = sigma(n^m * rad(n)^(m-1))/sigma(rad(n)^(m-1)) for n > 0 and m > 0, where sigma = A000203 and rad = A007947. - Velin Yanev, Aug 24 2017
• %A (verbatim): Olivier Gérard