cp's OEIS Frontend

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.

A306338 Carmichael numbers k such that phi(k) divides (k-1)*lambda(k).

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%I A306338 #27 Apr 22 2024 14:28:33
%S A306338 561,1105,1729,2465,6601,15841,41041,46657,52633,75361,115921,334153,
%T A306338 340561,658801,670033,2455921,2704801,4903921,5049001,6049681,6840001,
%U A306338 8355841,9439201,9582145,9613297,10402561,11119105,11205601,11972017,14469841,15888313,16778881
%N A306338 Carmichael numbers k such that phi(k) divides (k-1)*lambda(k).
%C A306338 Carmichael numbers k such that A034380(k) divides k-1.
%C A306338 A proper subset of Carmichael numbers in A173703.
%C A306338 The number of terms below 10^k for k=1,2,...,18 is 0, 0, 1, 5, 10, 15, 25, 56, 101, 184, 310, 508, 814, 1265, 1964, 2990, 4486, 6704. Cf. A055553.
%C A306338 Composite numbers k such that lcm(lambda(k),phi(k)/lambda(k)) divides k-1.
%C A306338 Problem: are there infinitely many such numbers?
%H A306338 Amiram Eldar, <a href="/A306338/b306338.txt">Table of n, a(n) for n = 1..10000</a>
%H A306338 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%t A306338 Select[Range[3, 100000, 2], !PrimeQ[#] && Divisible[#-1, c = CarmichaelLambda[#]] && Divisible[c*(#-1), EulerPhi[#]] &]
%Y A306338 Cf. A000010, A002322, A002997, A034380, A173703.
%K A306338 nonn
%O A306338 1,1
%A A306338 _Amiram Eldar_ and _Thomas Ordowski_, Feb 08 2019