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
Keywords
Examples
a(3) = (2^lambda(2*3 - 1) - 1)/(2*3 - 1) = (2^lambda(5) - 1)/5 = (2^4 - 1)/5 = 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.
Programs
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Mathematica
a[n_] := (2^CarmichaelLambda[n] - 1)/n; Table[a[n], {n, 1, 67, 2}]