

A048571


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


5



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, 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, 2, 3, 4, 4, 4, 4, 3, 2, 1, 0, 0, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 0
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OFFSET

0,13


LINKS



FORMULA



EXAMPLE

Triangle begins:
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
0,1,2,2,2,2,1,0
...


MATHEMATICA

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 *)
Table[PrimeNu[Binomial[n, k]], {n, 0, 15}, {k, 0, n}]//Flatten (* Harvey P. Dale, Jun 11 2019 *)


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



