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bibkey: pol2026a400194 authors: Omar E. Pol year: 2026 title: OEIS A400194, maximum length of a two-dense divisor block doi: null url: https://oeis.org/A400194 claim: “Conjecture: a(n) = A001511(n) * A400195(n).” strata_touched:

  • D5/S3/Factorization/TwoDenseDivisorBlockMaximum license: CC-BY-SA-4.0 triage: anchor

OEIS A400194

The Online Encyclopedia of Integer Sequences, A400194 revision 18, attributes the conjecture to Omar E. Pol. Its literal formula is:

Conjecture: a(n) = A001511(n) * A400195(n).

A400194 is the maximum of the A384222 block-length row. A400195 revision 16 counts the maximum number of odd terms in those same blocks. A384222 revision 120 and the defining programs split the complete increasing list of positive divisors at an adjacent pair a,b precisely when b>2a. Equality stays joined; singleton blocks are included. For positive n, A001511(n) is the ruler function v₂(n)+1.

The source JSON SHA-256 values are:

  • A400194 revision 18: c102e4755d69faa1534c8366d0cab9f1699f00e634a8116884590e001e19ae3c.
  • A400195 revision 16: 647a626770d88f013ebbf3e004af79fc26c764782f72f1f393062bde3b9a6a6d.
  • A384222 revision 120: 0e538b1434cbe6e28e36c3903c8ebd3afc17de70317697eb36c4c143e9e6c573.

Quoted OEIS content is attributed to the Online Encyclopedia of Integer Sequences and Omar E. Pol under CC-BY-SA-4.0. The mathematical discussion uses source facts and an independently checked ordinary argument; a literature search does not establish global priority.

Höft’s A384149 manuscript (2025-06-27), https://oeis.org/A384149/a384149.pdf, describes numeric aggregate sums and central dyadic chains. His Theorems Relating to Conjectures by Omar E. Pol (2026-03-21), https://oeis.org/A237270/a237270_4.pdf, gives a block/SRS correspondence and a restricted width-one chain corollary. These are relevant prior art for dyadic descriptions. Citation-only use of these manuscripts makes no claim that their numeric sum formulas alone give universal block cardinalities. The actual-block membership and bijection are necessary.

The bounded source qualification found no exact maximum formula supplier in the inspected D5 declarations, pinned Mathlib, selected third-party Lean sources, these manuscripts, or the inspected relevant OEIS entries. No exhaustive literature-absence or first-discovery claim follows.

Verified locator

  • URL: https://oeis.org/A400194
  • Same-family odd statistic: https://oeis.org/A400195
  • Block definition: https://oeis.org/A384222
  • Ruler function: https://oeis.org/A001511