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A048571 Triangle read by rows: T(n,k) = number of distinct prime factors of C(n,k). 5

%I

%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="http://www.ams.org/journals/mcom/1988-51-183/S0025-5718-1988-0942159-6/home.html">On prime divisors of binomial coefficients</a>, Math. Comp. 51 (1988), no. 183, 325-329.

%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.

%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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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)