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A339878 Carmichael numbers k such that phi(k) divides p*(k - 1) for some prime factor p of k - 1. 4
1729, 3069196417, 23915494401, 1334063001601, 6767608320001, 33812972024833, 1584348087168001, 1602991137369601, 6166793784729601, 1531757211193440001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first ten terms are all in A339818, none is in A339869, and all except a(2) and a(6) are in A339909.

Also, for all ten, a(n) == 1 (mod 64). (Cf. a similar comment in A338998).

LINKS

Table of n, a(n) for n=1..10.

Thomas Ordowski & Amiram Eldar, A new look at the Lehmer's totient problem, SeqFan, February 10 2019.

MATHEMATICA

carmichaels = Cases[Import["https://oeis.org/A002997/b002997.txt", "Table"], {_, _}][[;; , 2]]; q[n_] := Module[{p = FactorInteger[n - 1][[;; , 1]], phi = EulerPhi[n]}, AnyTrue[(n - 1)*p, Divisible[#, phi] &]]; Select[carmichaels, q] (* Amiram Eldar, Dec 26 2020 *)

CROSSREFS

Intersection of A002997 and A338998.

Cf. also A339818, A339869, A339909.

Sequence in context: A306657 A048949 A339909 * A258166 A130876 A234706

Adjacent sequences:  A339875 A339876 A339877 * A339879 A339880 A339881

KEYWORD

nonn,more

AUTHOR

Antti Karttunen (after Thomas Ordowski's and Amiram Eldar's SeqFan-posting), Dec 26 2020

EXTENSIONS

a(10) from Amiram Eldar, Dec 26 2020

STATUS

approved

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Last modified September 25 15:54 EDT 2022. Contains 356986 sequences. (Running on oeis4.)