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A005735 Greatest k such that binomial(k,n) has fewer than n distinct prime factors.
(Formerly M2719)
4

%I M2719

%S 1,3,8,14,32,62,87,169,132,367,389,510,394,512,512,1880,1880,1882,

%T 2099,1879,1885,2102,3470,3470,4805,4806,4806,3475,4806,4938,4939,

%U 5108,5119,6271,5122,5869,10663,10663,10663,7421,10667,10667,10668,11710,11711

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

%C 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

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

%H T. D. Noe, <a href="/A005735/b005735.txt">Table of n, a(n) for n=1..500</a>

%H Ernst S. Selmer, <a href="http://www.mscand.dk/article/viewFile/11662/9678">On the number of prime divisors of a binomial coefficient</a>, Math. Scand. 39 (1976), no. 2, 271-281.

%t 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 *)

%Y Cf. A005733, A129233.

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

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

%E Edited by _T. D. Noe_, Apr 05 2007

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Last modified October 18 05:22 EDT 2019. Contains 328146 sequences. (Running on oeis4.)