%I #9 Aug 03 2014 14:01:16

%S 0,0,1,1,2,2,2,2,3,3,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,7,8,8,7,7,8,8,

%T 9,9,9,9,10,10,10,10,10,10,11,10,10,10,10,10,10,11,11,11,12,12,12,13,

%U 13,13,13,13,13,12,13,14,14,14,14,15,15,14,14,14,15

%N Maximal number of distinct prime factors in binomial coefficients C(n,k) for k = 0,...,n.

%H T. D. Noe, <a href="/A048273/b048273.txt">Table of n, a(n) for n = 0..1000</a>

%e If n = 51 and k runs from 0 to 51, then a maximum of 11 distinct prime factors arise, for k = 20, 21, 22, 23, 28, 29, 30, 31.

%t Table[Max[Table[b = Binomial[n, k]; If[b == 1, 0, Length[FactorInteger[b]]], {k, 0, n}]], {n, 0, 100}] (* _T. D. Noe_, Apr 03 2012 *)

%Y Cf. A001405, A034973, A001221, A048571.

%K nonn

%O 0,5

%A _Labos Elemer_