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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
Pierre Goetgheluck, On prime divisors of binomial coefficients, Math. Comp. 51 (1988), no. 183, 325-329.
FORMULA
T(n, k) = A001221(A007318(n, k)). - Michel Marcus, Nov 04 2020
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
Sequence in context: A342955 A004197 A261684 * A025880 A058755 A128519
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane; edited Oct 06 2007 at the suggestion of T. D. Noe.
EXTENSIONS
Corrected by T. D. Noe, Oct 19 2007
STATUS
approved

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Last modified June 18 00:47 EDT 2024. Contains 373468 sequences. (Running on oeis4.)