A290484 - OEIS

%I #29 Feb 01 2024 00:26:32

%S 3,11,59,197,389,467,479,503,563,719,839,887,1523,1907,2087,2339,2837,

%T 3167,3989,4229,4259,4643,4679,4787,4903,4919,5417,5849,5879,6299,

%U 7307,7331,7577,7583,8117

%N Odd prime numbers that are factors of only one 3-Carmichael number.

%C Beeger proved in 1950 that if p < q < r are primes such that p*q*r is a 3-Carmichael number, then q < 2p^2 and r < p^3. Therefore there is a finite number of 3-Carmichael numbers which divisible by a given prime.

%C An odd prime p is a term if and only if A290481(A033270(p)) = 1. - _Max Alekseyev_, Jan 31 2024

%D N. G. W. H. Beeger, "On composite numbers n for which a^n == 1 (mod n) for every a prime to n", Scripta Mathematica, Vol. 16 (1950), pp. 133-135.

%H R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/carpsp.html">Tables relating to Carmichael numbers</a>.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_019.htm">Conjecture 19, A bound to the largest prime factor of certain Carmichael numbers</a>, The Prime Puzzles and Problems Connection.

%e 59 is in the sequence since it is a prime factor of only one 3-Carmichael number: 178837201 = 59 * 1451 * 2089.

%Y Cf. A065091 (Odd primes), A087788 (3-Carmichael numbers), A051663, A290481, A369777.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Aug 03 2017

%E a(1)-a(12) were calculated using Pinch's tables of Carmichael numbers (see links).

%E a(13)-a(35) from _Max Alekseyev_, Jan 31 2024