bibkey: noe2009a167857
authors: T. D. Noe
year: 2009
title: "OEIS A167857: Numbers whose divisors are represented by an integer polynomial"
doi: null
url: https://oeis.org/A167857
claim: "Are there terms with three distinct prime divisors?"
strata_touched:
  - D5/S3/Arith/SortedDivisorPolynomialThreePrimes
license: CC-BY-SA-4.0
triage: anchor

OEIS A167857

The Online Encyclopedia of Integer Sequences, entry author T. D. Noe, defines:

That is, these numbers n have the property that there is a polynomial f(x) with integer coefficients whose values at x=0..tau(n)-1 are the divisors of n, where tau(n) is the number of divisors of n.

It asks:

Are there terms with three distinct prime divisors?

The increasing example and the Mathematica Divisors/PARI divisors conventions fix increasing order. The sequence offset does not shift the polynomial inputs. The reference to A073103 as primes 210k+1 is inconsistent with that entry’s actual description and is excluded as a mathematical premise.

Attribution: The Online Encyclopedia of Integer Sequences, https://oeis.org/A167857, entry author T. D. Noe. Source license: CC-BY-SA-4.0, OEIS EULA oldid1653353. No source program is copied or executed.

Locator

Source URL: https://oeis.org/A167857. The anchors are the definition beginning “That is, these numbers n have the property…” and the exact question “Are there terms with three distinct prime divisors?” quoted above. The entry is the source of the question; the linked D5 resolution is repository-derived.

Official public/internal/history snapshots acquired at 2026-10-14T03:30:32Z display approved revision 5, Jan 29 2016 11:18:14 EST; displayed revision 1, Jun 01 2010, already contains the definition and question. Immutable revision views returned HTTP403, so these are dated source snapshots. Their SHA256 values are public 82b5d905e8b98a89867c59fad55bf78eff8cb96645debd431547a54e40da3208, internal 1cc4cb658e78caba633c2d7b24a93b16360b940d6f6850c9d35da9bfa5327b6c, and history 0ea60d6651a096ae4169606c0420b4d28bf2b4bcfd125645f0b74f186a162f50.