A163956 -id:A163956 - cp's OEIS frontend

A367231 Carmichael numbers k such that the multiplicative order of 2 modulo k is odd.

15841, 52633, 5049001, 68154001, 104852881, 238244041, 382536001, 3215031751, 3863326897, 7211236033, 8214723001, 15462960481, 22008493921, 23000028481, 29392867201, 31708772257, 41217865921, 53125756201, 60518537641, 74190097801, 77874636001, 83828294551, 103387371361

Offset: 1

Amiram Eldar, Nov 11 2023

nonn

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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Claude Goutier)
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
Index entries for sequences related to Carmichael numbers.

Intersection of A002997 and A036259.
Subsequence of A367230.
Cf. A002326, A163956.

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

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

A165139 Multiplicative order of 2 in Z/mZ with m=A104017(n).

Original entry on oeis.org

72, 264, 648, 600, 56, 720, 224, 2904, 600, 288, 648, 792, 4560, 180, 840, 792, 360, 1500, 1700, 324, 720, 360, 5152, 900, 576, 828, 4356, 26460, 19800, 144, 972, 700, 21780, 1152, 78408, 7128, 960, 540, 8064, 7968, 139080, 1620, 1296, 71148, 1960, 6624, 2280, 8820, 4680, 144, 495, 19800, 2016, 2592, 4356, 468, 1320, 3204, 2880

Offset: 1

A.K. Devaraj, Sep 05 2009

nonn

Cf. A104017, A162290, A163956.

Corrected and extended by M. F. Hasler, Sep 23 2009

Edited by N. J. A. Sloane, Sep 23 2009, following suggestions from M. F. Hasler

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A367231 Carmichael numbers k such that the multiplicative order of 2 modulo k is odd.

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A165139 Multiplicative order of 2 in Z/mZ with m=A104017(n).

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