A216911 - OEIS

%I #24 Feb 16 2025 08:33:18

%S 3,11,17,5,47,89,101,197,29,263,521,1559,173,3011,71,641,1277,53,317,

%T 4583,617,4019,401,3041,41,479,3347,131,10427,4643,1301,419,6689,5531,

%U 281,55217,251,2417,4001,491,1601,3137,449,3617,107,2969,4211,6737,1061

%N 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 Every term, other than a(1)=3, is a prime of the form 6*k - 1.

%H Charles R Greathouse IV, <a href="/A216911/b216911.txt">Table of n, a(n) for n = 1..3744</a>

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

%e The first few Carmichael numbers that are divisible by 3 (A258801), their prime factorizations, and the terms of this sequence are as follows:

%e .

%e   m | A258801(m) & prime factorization | prime factors not appearing earlier

%e   --+----------------------------------+----------------------------------------

%e   1 |        561 = 3 * 11 *  17        | a(1)  =    3,  a(2)  = 11,   a(3) = 17;

%e   2 |      62745 = 3 *  5 *  47 *   89 | a(4)  =    5,  a(5)  = 47,   a(6) = 89;

%e   3 |     656601 = 3 * 11 * 101 *  197 | a(7)  =  101,  a(8)  = 197; ...

%Y Cf. A002997 (Carmichael numbers), A258801 (Carmichael numbers divisible by 3).

%K nonn,changed

%O 1,1

%A _Marius Coman_, Sep 20 2012

%E a(26), a(34), a(43) corrected by _Charles R Greathouse IV_, Sep 20 2012