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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

T. D. Noe, Rows n=0..100 of triangle, flattened

Pierre Goetgheluck, On prime divisors of binomial coefficients, Math. Comp. 51 (1988), no. 183, 325-329.

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

Cf. A048273, A132896.

Sequence in context: A111143 A004197 A261684 * A025880 A058755 A128519

Adjacent sequences:  A048568 A048569 A048570 * A048572 A048573 A048574

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 April 6 20:17 EDT 2020. Contains 333286 sequences. (Running on oeis4.)