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A003139 Number of coprime chains with largest member n.
(Formerly M0129)
1
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 (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

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.

FORMULA

Entringer proves that log a(n) ~ sqrt(n). - Charles R Greathouse IV, Apr 24 2013

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 * A145652 A111248 A100714

Adjacent sequences:  A003136 A003137 A003138 * A003140 A003141 A003142

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 20 05:09 EDT 2013. Contains 226418 sequences.