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%I #61 Apr 22 2024 08:12:13
%S 0,0,0,2,4,9,19,51,107,219,417,757,1470,2666,5040,9280,17210,32039,
%T 59762,111811,210627,397968
%N Number of primary Carmichael numbers (A324316) less than 10^n.
%C The number of Carmichael numbers (A002997) less than 10^n is 0, 0, 1, 7, 16, 43, 105, 255, 646, 1547, 3605, 8241, 19279, 44706, 105212, 246683, 585355, 1401644, ... (see A055553).
%C The terms up to a(10) are given in Table 1 of Kellner and Sondow 2019. The terms up to a(18) and related results are given in Table 1.5 of Kellner 2019.
%C All computations depend on Pinch's database.
%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 Bernd C. Kellner and Jonathan Sondow, <a href="https://doi.org/10.4169/amer.math.monthly.124.8.695">Power-Sum Denominators</a>, Amer. Math. Monthly, 124 (2017), 695-709; <a href="https://arxiv.org/abs/1705.03857">arXiv preprint</a>, arXiv:1705.03857 [math.NT], 2017.
%H Bernd C. Kellner and Jonathan Sondow, <a href="http://math.colgate.edu/~integers/v52/v52.pdf">On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits</a>, Integers 21 (2021), #A52, 21 pp.; <a href="https://arxiv.org/abs/1902.10672">arXiv preprint</a>, arXiv:1902.10672 [math.NT], 2019-2021.
%H Bernd C. Kellner, <a href="http://math.colgate.edu/~integers/w38/w38.pdf">On primary Carmichael numbers</a>, Integers 22 (2022), #A38, 39 pp.; <a href="https://arxiv.org/abs/1902.11283">arXiv preprint</a>, arXiv:1902.11283 [math.NT], 2019-2022.
%H R. G. E. Pinch, <a href="http://www.s369624816.websitehome.co.uk/rgep/cartable.html">Tables relating to Carmichael numbers</a> (The Carmichael numbers up to 10^18, 2008).
%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%e There are two primary Carmichael numbers less than 10^4, namely, 1729 and 2821, so a(4) = 2.
%Y Cf. A002997, A055553, A324315, A324316, A324318, A324319, A324320, A324369, A324370, A324371, A324404, A324405.
%K nonn,base,more,hard
%O 1,4
%A _Bernd C. Kellner_ and _Jonathan Sondow_, Feb 22 2019
%E a(11)-a(18) from _Amiram Eldar_, Mar 01 2019
%E a(19) from _Amiram Eldar_, Dec 05 2020
%E a(20)-a(22) calculated using data from _Claude Goutier_ and added by _Amiram Eldar_, Apr 22 2024
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