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

1,1

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.

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.

Example

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.

Prog

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

Crossrefs

Cf. A002997, A006972.

Sequence in context: A247156 A320865 A274810 * A160405 A162032 A141621

Adjacent sequences: A329945 A329946 A329947 * A329949 A329950 A329951

Keyword

nonn,changed

Author

Daniel Suteu, Nov 25 2019

Status

approved