A324317 Number of primary Carmichael numbers (A324316) less than 10^n.

0, 0, 0, 2, 4, 9, 19, 51, 107, 219, 417, 757, 1470, 2666, 5040, 9280, 17210, 32039, 59762, 111811, 210627, 397968

Offset: 1

Author

Bernd C. Kellner and Jonathan Sondow, Feb 22 2019

Keywords

• nonn
• base
• more
• hard

Comments

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).

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.

All computations depend on Pinch's database.

Examples

			There are two primary Carmichael numbers less than 10^4, namely, 1729 and 2821, so a(4) = 2.
		

Links

• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, Amer. Math. Monthly, 124 (2017), 695-709; arXiv preprint, arXiv:1705.03857 [math.NT], 2017.
• Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, Integers 21 (2021), #A52, 21 pp.; arXiv preprint, arXiv:1902.10672 [math.NT], 2019-2021.
• Bernd C. Kellner, On primary Carmichael numbers, Integers 22 (2022), #A38, 39 pp.; arXiv preprint, arXiv:1902.11283 [math.NT], 2019-2022.
• R. G. E. Pinch, Tables relating to Carmichael numbers (The Carmichael numbers up to 10^18, 2008).
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A002997, A055553, A324315, A324316, A324318, A324319, A324320, A324369, A324370, A324371, A324404, A324405.

Extensions

a(11)-a(18) from Amiram Eldar, Mar 01 2019

a(19) from Amiram Eldar, Dec 05 2020

a(20)-a(22) calculated using data from Claude Goutier and added by Amiram Eldar, Apr 22 2024