OFFSET
1,1
COMMENTS
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.
REFERENCES
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.
LINKS
R. G. E. Pinch, Tables relating to Carmichael numbers.
Carlos Rivera, Conjecture 19, A bound to the largest prime factor of certain Carmichael numbers, The Prime Puzzles and Problems Connection.
EXAMPLE
59 is in the sequence since it is a prime factor of only one 3-Carmichael number: 178837201 = 59 * 1451 * 2089.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Aug 03 2017
EXTENSIONS
a(1)-a(12) were calculated using Pinch's tables of Carmichael numbers (see links).
a(13)-a(35) from Max Alekseyev, Jan 31 2024
STATUS
approved