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A290481
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The number of 3-Carmichael numbers that are divisible by the n-th odd prime.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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).
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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