A003140 Number of coprime chains with largest member prime(n). (Formerly M0896)

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

Charlie Neder, Table of n, a(n) for n = 1..62

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

Adjacent sequences: A003137 A003138 A003139 * A003141 A003142 A003143

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

a(31)-a(44) from Charlie Neder, Dec 15 2018

Status

approved