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%I #20 Nov 04 2020 05:23:11
%S 0,0,0,0,1,0,0,1,1,0,0,1,2,1,0,0,1,2,2,1,0,0,2,2,2,2,2,0,0,1,2,2,2,2,
%T 1,0,0,1,2,2,3,2,2,1,0,0,1,2,3,3,3,3,2,1,0,0,2,2,3,4,3,4,3,2,2,0,0,1,
%U 2,3,4,4,4,4,3,2,1,0,0,2,3,3,3,3,4,3,3,3,3,2,0
%N Triangle read by rows: T(n,k) = number of distinct prime factors of C(n,k).
%H T. D. Noe, <a href="/A048571/b048571.txt">Rows n=0..100 of triangle, flattened</a>
%H Pierre Goetgheluck, <a href="https://doi.org/10.1090/S0025-5718-1988-0942159-6">On prime divisors of binomial coefficients</a>, Math. Comp. 51 (1988), no. 183, 325-329.
%F T(n, k) = A001221(A007318(n, k)). - _Michel Marcus_, Nov 04 2020
%e Triangle begins:
%e 0
%e 0,0
%e 0,1,0
%e 0,1,1,0
%e 0,1,2,1,0
%e 0,1,2,2,1,0
%e 0,2,2,2,2,2,0
%e 0,1,2,2,2,2,1,0
%e ...
%t Flatten[Table[b=Binomial[n,k]; If[b==1, 0, Length[FactorInteger[b]]], {n,0,12}, {k,0,n}]] (* _T. D. Noe_, Oct 19 2007, Apr 03 2012 *)
%t Table[PrimeNu[Binomial[n,k]],{n,0,15},{k,0,n}]//Flatten (* _Harvey P. Dale_, Jun 11 2019 *)
%Y Cf. A048273, A132896.
%Y Cf. A001221, A007318.
%K nonn,tabl
%O 0,13
%A _N. J. A. Sloane_; edited Oct 06 2007 at the suggestion of T. D. Noe.
%E Corrected by _T. D. Noe_, Oct 19 2007
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