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A290481
The number of 3-Carmichael numbers that are divisible by the n-th odd prime.
4
1, 3, 6, 1, 8, 5, 4, 2, 4, 9, 8, 9, 12, 3, 3, 1, 16, 4, 7, 11, 2, 2, 5, 8, 4, 6, 3, 12, 6, 8, 11, 5, 6, 2, 11, 14, 8, 2, 3, 4, 15, 6, 11, 1, 9, 22, 5, 4, 7, 2, 5, 15, 8, 6, 4, 4, 21, 9, 10, 2, 5, 12, 9, 20, 2, 20, 19, 2, 6, 8, 2, 9, 8, 12, 3, 1, 10, 14, 10, 3
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
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
Cf. A065091 (Odd primes), A087788 (3-Carmichael numbers).
Sequence in context: A096602 A288853 A296184 * A259501 A118948 A176092
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 03 2017
STATUS
approved