A329948 Carmichael numbers m that have at least 3 prime factors p such that p+1 | m+1.

9857524690572481, 33439671284716801, 96653613831890401, 270136961300544031, 528096456788419441, 650643395658753601, 710238404427321601, 1822922951416158241, 4011563714063821201, 4525693104167627041, 4631812281009523441, 7049793086137296001, 8605736094003523201, 10449416165574628801, 11175581620177915681, 12746447178170148001, 12769123623410580481, 17705945296667070001

Offset: 1

Author

Daniel Suteu, Nov 25 2019

Keywords

• nonn

Comments

It is not known whether any Carmichael number (A002997) is also Lucas-Carmichael number (A006972). If such a number exists, then it would be a term of this sequence.

Examples

			m = 9857524690572481 is a term because it is a Carmichael number and it has at least 3 prime factors p, {13, 61, 433}, such that p+1 | m+1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..179 (terms below 10^22, calculated using data from Claude Goutier)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Wikipedia, Carmichael number.
• Wikipedia, Lucas-Carmichael number.

Crossrefs

Cf. A002997, A006972.

Programs

Perl

use bigint; use ntheory ':all'; sub isok { my $m = $[0]; is_carmichael($m) && (grep { ($m+1) % ($+1) == 0 } factor($m)) >= 3 };