A306657 Least primary Carmichael number (A324316) with n prime factors, or -1 if no such number exists.

1729, 10606681, 4872420815346001

Offset: 3

Author

Bernd C. Kellner and Jonathan Sondow, Mar 03 2019

Keywords

• nonn
• hard
• more
• bref

Comments

Primary Carmichael numbers were introduced in Kellner and Sondow 2019. For this sequence, see Kellner 2019.

Conjecture: the sequence is infinite.

a(6) > 10^22, if it exists. - Amiram Eldar, Apr 22 2024

Examples

			1729 = 7 * 13 * 19,
10606681 = 31 * 43 * 73 * 109,
4872420815346001 = 211 * 239 * 379 * 10711 * 23801.
		

Links

• 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.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Least Carmichael number with n prime factors is A006931.

Cf. also A002997, A324316.

Extensions

Escape clause added by Amiram Eldar, Apr 22 2024