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A003139
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Number of coprime chains with largest member n.
(Formerly M0129)
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1
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1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 9, 1, 10, 2, 4, 3, 19, 1, 20, 2, 6, 4, 32, 1, 21, 7, 16, 7, 84, 1, 85, 9, 18, 11, 35, 3, 161, 15, 30, 6, 212, 2, 214, 15, 12, 19, 260, 3, 154, 11, 62, 31, 521, 5, 129
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OFFSET
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1,5
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COMMENTS
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A coprime chain is a nonempty set of integers greater than 1 such that all primes <= the largest member divide exactly one term of the set. - Charles R Greathouse IV, Apr 24 2013
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..55.
R. C. Entringer, The number of coprime chains with largest member n, Proc. Amer. Math. Soc., 16 (1965), 806-810.
R. C. Entringer, Some properties of certain sets of coprime integers, Proc. Amer. Math. Soc. 16 (1965), 515-521.
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FORMULA
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Entringer proves that log a(n) ~ sqrt(n). - Charles R Greathouse IV, Apr 24 2013
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PROG
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(PARI) isCC(v)=forprime(p=2, vecmax(v), if(sum(i=1, #v, v[i]%p==0)!=1, return(0))); 1
a(n)=my(v=vector(n-1, i, i+1)); sum(i=2^(n-2), 2^(n-1)-1, isCC(vecextract(v, i))) \\ Charles R Greathouse IV, Apr 24 2013
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CROSSREFS
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Cf. A003140.
Sequence in context: A224762 A039776 A048864 * A145652 A111248 A100714
Adjacent sequences: A003136 A003137 A003138 * A003140 A003141 A003142
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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