A329948 - OEIS

%I #13 Apr 21 2024 10:00:00

%S 9857524690572481,33439671284716801,96653613831890401,

%T 270136961300544031,528096456788419441,650643395658753601,

%U 710238404427321601,1822922951416158241,4011563714063821201,4525693104167627041,4631812281009523441,7049793086137296001,8605736094003523201,10449416165574628801,11175581620177915681,12746447178170148001,12769123623410580481,17705945296667070001

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

%C 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.

%H Amiram Eldar, <a href="/A329948/b329948.txt">Table of n, a(n) for n = 1..179</a> (terms below 10^22, calculated using data from Claude Goutier)

%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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Carmichael_number">Carmichael number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael_number">Lucas-Carmichael number</a>.

%e 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.

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

%Y Cf. A002997, A006972.

%K nonn

%O 1,1

%A _Daniel Suteu_, Nov 25 2019