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 A003139 Number of coprime chains with largest member n. (Formerly M0129) 2
 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, 19, 90, 54, 818, 2, 820, 54, 44, 57, 207, 7, 1189, 62, 147, 8, 1406 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Charlie Neder, Table of n, a(n) for n = 1..299 R. C. Entringer, The number of coprime chains with largest member n, Proc. Amer. Math. Soc., 16 (1965), 806-810. R. C. Entringer, The number of coprime chains with largest member n, Proc. Amer. Math. Soc., 16 (1965), 806-810. [Annotated scanned copy] R. C. Entringer, Some properties of certain sets of coprime integers, Proc. Amer. Math. Soc. 16 (1965), 515-521. FORMULA Entringer proves that log a(n) ~ sqrt(n). - Charles R Greathouse IV, Apr 24 2013 If p and q are consecutive primes with q > p, then a(q) = a(q-1) + a(q-2) + ... + a(p). - Charlie Neder, Dec 15 2018 EXAMPLE The a(11) = 9 coprime chains with largest element 11 are {2,3,5,7,11}, {2,5,7,9,11}, {3,4,5,7,11}, {3,5,7,8,11}, {3,7,10,11}, {4,5,7,9,11}, {5,6,7,11}, {5,7,8,9,11}, and {7,9,10,11}. - Charlie Neder, Dec 15 2018 PROG (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 CROSSREFS Cf. A003140. Sequence in context: A224762 A039776 A048864 * A349918 A244797 A308659 Adjacent sequences:  A003136 A003137 A003138 * A003140 A003141 A003142 KEYWORD nonn,nice AUTHOR EXTENSIONS a(56)-a(71) from Charlie Neder, Dec 15 2018 STATUS approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)