bibkey: karttunen2007a129598
authors: Antti Karttunen
year: 2007
title: "OEIS A129598, a(n) = n * A111089(n)"
doi: null
url: https://oeis.org/A129598
claim: "A129598 %N: a(n) = n * A111089(n). A129598 %C: Conjecture: differs from A050399 at the positions given by A089966. E.g., a(15)=75, instead of A050399(15)=225, a(30)=150, instead of A050399(30)=450, a(33)=363, instead of A050399(33)=1089, a(45)=225, instead of A050399(45)=1225. - _Antti Karttunen_, May 01 2007"
strata_touched:
  - D5/S0/Certificates/KarttunenGcdTotientPositionRefutation
license: citation-only
triage: anchor

OEIS A129598

The NAME of A129598 states:

a(n) = n * A111089(n).

Antti Karttunen’s COMMENT of May 1, 2007 states:

Conjecture: differs from A050399 at the positions given by A089966. E.g., a(15)=75, instead of A050399(15)=225, a(30)=150, instead of A050399(30)=450, a(33)=363, instead of A050399(33)=1089, a(45)=225, instead of A050399(45)=1225.

The NAME of A050399 states:

Least k such that n = A009195(k) (= gcd(phi(k), k)).

The NAME of A089966 states:

Numbers k such that omega(k) = gpf(k) mod lpf(k), where omega=A001221, gpf=A006530 and lpf=A020639.

The AUTHOR line is:

Antti Karttunen, May 01 2007

Verified locator

• URL: https://oeis.org/A129598
• A129598 NAME (verbatim): a(n) = n * A111089(n).
• A129598 COMMENT, Conjecture 1 (verbatim): Conjecture: differs from A050399 at the positions given by A089966. E.g., a(15)=75, instead of A050399(15)=225, a(30)=150, instead of A050399(30)=450, a(33)=363, instead of A050399(33)=1089, a(45)=225, instead of A050399(45)=1225.
• A050399 NAME (verbatim): Least k such that n = A009195(k) (= gcd(phi(k), k)).
• A089966 NAME (verbatim): Numbers k such that omega(k) = gpf(k) mod lpf(k), where omega=A001221, gpf=A006530 and lpf=A020639.
• AUTHOR (verbatim): Antti Karttunen, May 01 2007

Only Conjecture 1 is refuted: at 60, a(60)=300 is not a gcd-phi preimage of 60, so a(60) differs from b(60), while 60 is not in A089966. A089966’s published data contains 15, 33, and 45 but not 30, so Karttunen’s listed example at 30 is inconsistent with the referenced sequence data.