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Carmichael numbers of the form (6*k + 1)*(24*k + 1)*(30*k + 1).
3

%I #23 Apr 22 2024 13:44:09

%S 126217,68154001,1828377001,3713287801,27388362001,32071969801,

%T 63593140801,113267783377,122666876401,193403531401,227959335001,

%U 246682590001,910355497801,1389020532001,4790779641001,5367929037001,6486222838801,24572944746001

%N Carmichael numbers of the form (6*k + 1)*(24*k + 1)*(30*k + 1).

%C These numbers:

%C - are pseudoprimes to bases 2, 3 and 5;

%C - do not occur in A097130 (Carmichael numbers that are not == 1 mod 24).

%C The number (6*k + 1)*(24*k + 1)*(30*k + 1) is in the sequence if:

%C - k is congruent to 5 mod 10;

%C - its three factors are all prime.

%H Amiram Eldar, <a href="/A230722/b230722.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>.

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>.

%o (Magma) [a : k in [1..1785 by 2] | IsOne(a mod CarmichaelLambda(a)) where a is (6*k+1)*(24*k+1)*(30*k+1)]

%Y Subsequence of A002997 and of A083737.

%Y Supersequence of A230746.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Oct 28 2013