This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338998 #46 Feb 16 2025 08:34:01
%S A338998 1729,12801,5079361,34479361,3069196417,23915494401
%N A338998 Composite numbers k such that phi(k) divides p*(k - 1) for some prime factor p of k - 1.
%C A338998 All terms of this sequence are terms of A337316 and all Lehmer numbers (if there are any) are contained in this sequence.
%C A338998 Terms 1729 and 3069196417 and several others are also Carmichael numbers (A002997), they are given in A339878.
%C A338998 The sequence also includes: 1334063001601, 6767608320001, 33812972024833, 380655711289345, 1584348087168001, 1602991137369601, 6166793784729601, 1531757211193440001. - _Daniel Suteu_, Nov 24 2020
%C A338998 Apparently, a(n) == 1 (mod 64). - _Hugo Pfoertner_, Dec 08 2020
%C A338998 The "Lehmer numbers" above refers to composite 1-Lehmer numbers, that is, numbers n that would satisfy the equation y * phi(n) = n-1, for some integer y > 1. Lehmer conjectured that no such numbers exist. See the assorted Web-links. - _Antti Karttunen_, Dec 26 2020
%H A338998 D. H. Lehmer, <a href="https://doi.org/10.1090/S0002-9904-1932-05521-5">On Euler's totient function</a>, Bulletin of the American Mathematical Society, 38 (1932), 745-751.
%H A338998 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Lehmer_number/">k-Lehmer numbers</a>
%H A338998 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LehmersTotientProblem.html">Lehmer's Totient Problem</a>
%H A338998 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lehmer's_totient_problem">Lehmer's totient problem</a>
%e A338998 phi(1729) = 1296 divides 3 * 1728.
%o A338998 (PARI) is(n)={my(s=denominator((n-1)/eulerphi(n))); !isprime(n) && isprime(s) && ((n-1)%s==0) && n>1}
%o A338998 { forcomposite(n=1, 2^32, if(is(n), print1(n, ", "))) }
%Y A338998 Subsequence of A173703 (2-Lehmer numbers).
%Y A338998 Cf. A337316 (with "squarefree divisor" instead of "prime factor").
%Y A338998 Cf. A000010 (phi), A238574 (k-Lehmer numbers for some k), A339878 (Carmichael numbers in this sequence).
%K A338998 nonn,more
%O A338998 1,1
%A A338998 _Tomohiro Yamada_, Nov 18 2020
%E A338998 a(5) from _Amiram Eldar_, Nov 18 2020
%E A338998 a(6) from _Daniel Suteu_, confirmed by _Max Alekseyev_, Sep 29 2023