A005735 Greatest k such that binomial(k,n) has fewer than n distinct prime factors. (Formerly M2719)

1, 3, 8, 14, 32, 62, 87, 169, 132, 367, 389, 510, 394, 512, 512, 1880, 1880, 1882, 2099, 1879, 1885, 2102, 3470, 3470, 4805, 4806, 4806, 3475, 4806, 4938, 4939, 5108, 5119, 6271, 5122, 5869, 10663, 10663, 10663, 7421, 10667, 10667, 10668, 11710, 11711

Offset

1,2

Comments

Table 2 in Selmer's paper has a typo for n = 76. Selmer "cheats" to find a(n) for n>27. - T. D. Noe, Apr 05 2007

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..500

Ernst S. Selmer, On the number of prime divisors of a binomial coefficient, Math. Scand. 39 (1976), no. 2, 271-281.

Mathematica

Join[{1}, Table[n=k; b=1; n0=Infinity; While[n++; b=b*n/(n-k); If[Length[FactorInteger[b]]<k, n0=n]; n<10*n0]; n0, {k, 2, 30}]] (* T. D. Noe, Apr 05 2007 *)

Crossrefs

Cf. A005733, A129233.

Sequence in context: A340627 A350520 A168155 * A208436 A297015 A135872

Adjacent sequences: A005732 A005733 A005734 * A005736 A005737 A005738

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 26 2004

Edited by T. D. Noe, Apr 05 2007

Status

approved