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Number of rows of Pascal's triangle in which the maximal number of prime factors is n.
0

%I #5 Jul 27 2012 17:32:18

%S 2,2,4,2,6,4,7,3,4,4,12,4,4,7,7,6,8,5,9,5,10,5,10,6,7,8,6,9,5,11,4,8,

%T 10,7,5,11,13,6,10,9,9,9,9,5,5,9,12,7,11,4,15,7,2,8,12,13,7,6,13,6,13,

%U 16,7,7,8,15,9,6,6,7,4,16,6,5,20,4,11,11,6,16

%N Number of rows of Pascal's triangle in which the maximal number of prime factors is n.

%e As can be seen in A048273, there are 6 rows of binomial coefficients in which the maximum number of prime factors is 4: rows 10 to 15.

%t nn = 50; t = Table[0, {nn + 1}]; n = -1; f = 0; While[f < 10, n++; m = Max[Table[b = Binomial[n, k]; If[b == 1, 0, Length[FactorInteger[b]]], {k, 0, n}]]; If[0 <= m <= nn, t[[m + 1]]++; f = 0, f++]]; t

%Y Cf. A048273.

%K nonn

%O 0,1

%A _T. D. Noe_, Apr 03 2012