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Carmichael numbers k such that 2^d == 2^(k/d) (mod k) for all d|k.
1

%I #23 Apr 22 2024 08:12:22

%S 1105,294409,852841,3828001,17098369,118901521,150846961,172947529,

%T 186393481,200753281,686059921,771043201,1001152801,1207252621,

%U 1269295201,1299963601,1632785701,1772267281,2301745249,4215885697,4562359201,4765950001,4897161361

%N Carmichael numbers k such that 2^d == 2^(k/d) (mod k) for all d|k.

%C Intersection of A002997 and A291601.

%H Amiram Eldar, <a href="/A291616/b291616.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier; terms 1..3648 from Max Alekseyev)

%H Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.

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

%e Carmichael number 294409 = 37*73*109 is a term because 2^37 == 2^(73*109) (mod 294409), 2^73 == 2^(37*109) (mod 294409), 2^109 == 2^(37*73) (mod 294409).

%Y Cf. A002997, A291601, A291612.

%K nonn

%O 1,1

%A _Max Alekseyev_, _Thomas Ordowski_, _Altug Alkan_, Aug 28 2017