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A289337
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Composite numbers (pseudoprimes) n, that are not Carmichael numbers, such that A000670(n-1) == 0 (mod n).
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1
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OFFSET
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1,1
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COMMENTS
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I. J. Good proved that A000670(k*(p-1)) == 0 (mod p) for all k >= 1 and prime p. Therefore the congruence A000670(n-1) == 0 (mod n) holds for all primes and Carmichael numbers. This sequence consist of the other composite numbers for which the congruence holds.
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LINKS
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EXAMPLE
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A000670(24) = 2958279121074145472650648875 is divisible by 25 and 25 is not a prime, nor a Carmichael number.
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]*a[n - k], {k, 1, n}]; carmichaelQ[n_]:=(Mod[n, CarmichaelLambda[n]] == 1); seqQ[n_] := !carmichaelQ[n] && Divisible[a[n-1], n]; Select[Range[2, 500], seqQ]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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