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A003140
Number of coprime chains with largest member prime(n).
(Formerly M0896)
2
1, 1, 2, 3, 9, 10, 19, 20, 32, 84, 85, 161, 212, 214, 260, 521, 818, 820, 1189, 1406, 1415, 2005, 2375, 3351, 5698, 6122, 6141, 6600, 6623, 7270, 23993, 26735, 33686, 33753, 55735, 55750, 66498, 85117, 90310, 147374, 165450, 165479, 249822, 250176
OFFSET
1,3
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
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.
PROG
(PARI) isCC(v)=forprime(p=2, vecmax(v), if(sum(i=1, #v, v[i]%p==0)!=1, return(0))); 1
A003139(n)=my(v=vector(n-1, i, i+1)); sum(i=2^(n-2), 2^(n-1)-1, isCC(vecextract(v, i)))
a(n)=if(n<3, return(1)); my(p=prime(n)); sum(k=precprime(p-1), p-1, A003139(k)) \\ Charles R Greathouse IV, Apr 24 2013
CROSSREFS
Cf. A003139.
Sequence in context: A280731 A353614 A352198 * A057234 A109636 A057236
KEYWORD
nonn,nice
EXTENSIONS
a(31)-a(44) from Charlie Neder, Dec 15 2018
STATUS
approved