

A048273


Maximal number of distinct prime factors in binomial coefficients C(n,k) for k = 0,...,n.


10



0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 12, 13, 14, 14, 14, 14, 15, 15, 14, 14, 14, 15
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OFFSET

0,5


LINKS



EXAMPLE

If n = 51 and k runs from 0 to 51, then a maximum of 11 distinct prime factors arise, for k = 20, 21, 22, 23, 28, 29, 30, 31.


MATHEMATICA

Table[Max[Table[b = Binomial[n, k]; If[b == 1, 0, Length[FactorInteger[b]]], {k, 0, n}]], {n, 0, 100}] (* T. D. Noe, Apr 03 2012 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



