A329238 Carmichael quotients to base 2: a(n) = (2^lambda(2*n-1)-1)/(2*n-1), where lambda is the Carmichael lambda function (A002322).

1, 1, 3, 9, 7, 93, 315, 1, 3855, 13797, 3, 182361, 41943, 9709, 9256395, 34636833, 31, 117, 1857283155, 105, 26817356775, 102280151421, 91, 1497207322929, 89756051247, 1285, 84973577874915, 19065, 4599, 4885260612740877, 18900352534538475, 1, 63, 1101298153654301589

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..1671

Florian Luca, Min Sha, and Igor E. Shparlinski On two functions arising in the study of the Euler and Carmichael quotients, Colloquium Mathematicum, Vol. 149, No. 2 (2017), pp. 179-192, arXiv preprint, arXiv:1705.00388 [math.NT] (2017).

Min Sha, The arithmetic of Carmichael quotients, Periodica Mathematica Hungarica, Vol. 71, No. 1 (2015), pp. 11-23, Correction to: The arithmetic of Carmichael quotients, ibid., Vol. 76, No. 2 (2018), pp. 271-273, preprint, arXiv:1108.2579v7 [math.NT] (2011-2017).

Chenhuang Wu, Zhixiong Chen, and Xiaoni Du, Binary threshold sequences derived from Carmichael quotients with even numbers modulus, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. 95, No. 7 (2012), pp. 1197-1199, alternative link.

Example

a(3) = (2^lambda(2*3 - 1) - 1)/(2*3 - 1) = (2^lambda(5) - 1)/5 = (2^4 - 1)/5 = 3.

Mathematica

a[n_] := (2^CarmichaelLambda[n] - 1)/n; Table[a[n], {n, 1, 67, 2}]

Crossrefs

Cf. A001226, A002322, A007663.

Sequence in context: A302158 A337974 A137299 * A001226 A338402 A093498

Adjacent sequences: A329235 A329236 A329237 * A329239 A329240 A329241

Keyword

nonn

Author

Amiram Eldar, Nov 08 2019

Status

approved