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A290484
Odd prime numbers that are factors of only one 3-Carmichael number.
1
3, 11, 59, 197, 389, 467, 479, 503, 563, 719, 839, 887, 1523, 1907, 2087, 2339, 2837, 3167, 3989, 4229, 4259, 4643, 4679, 4787, 4903, 4919, 5417, 5849, 5879, 6299, 7307, 7331, 7577, 7583, 8117
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.
An odd prime p is a term if and only if A290481(A033270(p)) = 1. - Max Alekseyev, Jan 31 2024
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.
EXAMPLE
59 is in the sequence since it is a prime factor of only one 3-Carmichael number: 178837201 = 59 * 1451 * 2089.
CROSSREFS
Cf. A065091 (Odd primes), A087788 (3-Carmichael numbers), A051663, A290481, A369777.
Sequence in context: A375912 A319248 A340865 * A156560 A028342 A137982
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