bibkey: israeloudra2020a274010
authors: Robert Israel; Ridouane Oudra
year: 2020
title: "OEIS A274010: the Boris Stechkin function and an adjacent divisor-count formula"
doi: null
url: https://oeis.org/A274010
claim: "Conjecture: a(n) = tau(n) + tau(n-1) - 2, for n>=2."
strata_touched:
  - D5/S3/Arith/StechkinFunctionDivisorCount
license: citation-only
triage: anchor

OEIS A274010 and the Stechkin function

Robert Israel’s 2016 entry defines the Boris Stechkin function a(n) as the number of integers m with 2 <= m <= n for which m-1 divides the floor of n(m-1)/m. Ridouane Oudra added the adjacent divisor-count conjecture on February 28, 2020:

Conjecture: a(n) = tau(n) + tau(n-1) - 2, for n>=2.

Here tau is the number of positive divisors. Natural-number Euclidean division realizes the floor in the defining predicate. For n >= 2, both n and n-1 have the divisor one, so the sum of their divisor counts is at least two. Consequently the subtraction-free equality with two added to the left is equivalent to the displayed integer-subtraction formula.

Verified locator

• URL: https://oeis.org/A274010
• %I (verbatim): A274010 #19 Mar 01 2020 12:13:16
• %N (verbatim): Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m-1)/m) divisible by m-1.
• %F (verbatim): Conjecture: a(n) = tau(n) + tau(n-1) - 2, for n>=2. - Ridouane Oudra, Feb 28 2020
• %A (verbatim): Robert Israel, Jun 06 2016

Search boundary

The entry has no settlement line. Its bibliography predates the conjecture, and its hyperlink section contains a table rather than a proof source. The issue registration records zero exact arXiv hits for the phrase “Stechkin function” with positive-control searches, and zero exact repository or pinned Mathlib hits for the sequence name and formula. Those bounded searches do not establish global priority or exclude differently indexed results.