A367231 - OEIS

%I #15 Apr 22 2024 13:47:56

%S 15841,52633,5049001,68154001,104852881,238244041,382536001,

%T 3215031751,3863326897,7211236033,8214723001,15462960481,22008493921,

%U 23000028481,29392867201,31708772257,41217865921,53125756201,60518537641,74190097801,77874636001,83828294551,103387371361

%N Carmichael numbers k such that the multiplicative order of 2 modulo k is odd.

%C These Carmichael numbers seem to be relatively rare: among the 4279356 Carmichael numbers below 2^64 only 3097 are terms of this sequence.	

%H Amiram Eldar, <a href="/A367231/b367231.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier)

%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>.

%t Select[2*Range[3*10^6] + 1, Mod[#, CarmichaelLambda[#]] == 1 && CompositeQ[#] && OddQ[MultiplicativeOrder[2, #]] &]

%o (PARI) is(n) = n > 1 && n % 2 && !isprime(n) && n % lcm(znstar(n)[2]) == 1 && znorder(Mod(2, n)) % 2;

%Y Intersection of A002997 and A036259.

%Y Subsequence of A367230.

%Y Cf. A002326, A163956.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 11 2023