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A216911 Numbers that are a prime factor of a Carmichael number divisible by 3, listed in the order in which they appear in the prime factorizations of such Carmichael numbers.

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%I A216911 #24 Feb 16 2025 08:33:18
%S A216911 3,11,17,5,47,89,101,197,29,263,521,1559,173,3011,71,641,1277,53,317,
%T A216911 4583,617,4019,401,3041,41,479,3347,131,10427,4643,1301,419,6689,5531,
%U A216911 281,55217,251,2417,4001,491,1601,3137,449,3617,107,2969,4211,6737,1061
%N A216911 Numbers that are a prime factor of a Carmichael number divisible by 3, listed in the order in which they appear in the prime factorizations of such Carmichael numbers.
%C A216911 Every term, other than a(1)=3, is a prime of the form 6*k - 1.
%H A216911 Charles R Greathouse IV, <a href="/A216911/b216911.txt">Table of n, a(n) for n = 1..3744</a>
%H A216911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>
%e A216911 The first few Carmichael numbers that are divisible by 3 (A258801), their prime factorizations, and the terms of this sequence are as follows:
%e A216911 .
%e A216911   m | A258801(m) & prime factorization | prime factors not appearing earlier
%e A216911   --+----------------------------------+----------------------------------------
%e A216911   1 |        561 = 3 * 11 *  17        | a(1)  =    3,  a(2)  = 11,   a(3) = 17;
%e A216911   2 |      62745 = 3 *  5 *  47 *   89 | a(4)  =    5,  a(5)  = 47,   a(6) = 89;
%e A216911   3 |     656601 = 3 * 11 * 101 *  197 | a(7)  =  101,  a(8)  = 197; ...
%Y A216911 Cf. A002997 (Carmichael numbers), A258801 (Carmichael numbers divisible by 3).
%K A216911 nonn
%O A216911 1,1
%A A216911 _Marius Coman_, Sep 20 2012
%E A216911 a(26), a(34), a(43) corrected by _Charles R Greathouse IV_, Sep 20 2012