OFFSET
1,2
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 the number of 3-Carmichael numbers that are divisible by a fixed prime is finite.
The terms were calculated using Pinch's tables of Carmichael numbers (see link below).
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
Max Alekseyev, Table of n, a(n) for n = 1..1000
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
There is only one 3-Carmichael number that is divisible by 3 (561); there are three that are divisible by 5 (1105, 2465 and 10585) and six that are divisible by 7 (1729, 2821, 6601, 8911, 15841 and 52633). Thus a(1)=1, a(2)=3 and a(3)=6.
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 03 2017
STATUS
approved