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A230722 Carmichael numbers of the form (6*k + 1)*(24*k + 1)*(30*k + 1).

%I A230722 #24 Feb 16 2025 08:33:20
%S A230722 126217,68154001,1828377001,3713287801,27388362001,32071969801,
%T A230722 63593140801,113267783377,122666876401,193403531401,227959335001,
%U A230722 246682590001,910355497801,1389020532001,4790779641001,5367929037001,6486222838801,24572944746001
%N A230722 Carmichael numbers of the form (6*k + 1)*(24*k + 1)*(30*k + 1).
%C A230722 These numbers:
%C A230722 - are pseudoprimes to bases 2, 3 and 5;
%C A230722 - do not occur in A097130 (Carmichael numbers that are not == 1 mod 24).
%C A230722 The number (6*k + 1)*(24*k + 1)*(30*k + 1) is in the sequence if:
%C A230722 - k is congruent to 5 mod 10;
%C A230722 - its three factors are all prime.
%H A230722 Amiram Eldar, <a href="/A230722/b230722.txt">Table of n, a(n) for n = 1..10000</a>
%H A230722 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>.
%H A230722 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%H A230722 <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>.
%o A230722 (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 A230722 Subsequence of A002997 and of A083737.
%Y A230722 Supersequence of A230746.
%K A230722 nonn
%O A230722 1,1
%A A230722 _Arkadiusz Wesolowski_, Oct 28 2013