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

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A005733, A129233.

Programs

Mathematica

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

Extensions

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

Edited by T. D. Noe, Apr 05 2007