A004788 - OEIS

%I #28 Apr 01 2018 21:01:32

%S 0,0,1,1,2,2,3,3,3,3,4,5,5,5,5,5,6,6,7,7,7,7,8,9,8,8,8,8,9,10,10,10,

%T 10,10,10,11,11,11,11,12,12,12,13,13,14,13,14,15,14,14,14,14,15,15,15,

%U 16,15,15,16,17,17,17,18,17,17,17,18,18,18,19,19,20,20

%N Number of distinct prime divisors of the numbers in row n of Pascal's triangle.

%C Also the number of prime divisors of A002944(n) = lcm_{j=0..floor(n/2)} binomial(n,j).

%C The terms are increasing by intervals, then decrease once. The local maxima are obtained for 23, 44, 47, 55, 62, 79, 83, 89, 104, 119, 131, 134, 139, 143, .... - _Michel Marcus_, Mar 21 2013

%C a(A004789(n)) = n and a(m) != n for m < A004789(n). - _Reinhard Zumkeller_, Mar 16 2015

%H T. D. Noe, <a href="/A004788/b004788.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A001221(A001142(n)). - _Reinhard Zumkeller_, Mar 16 2015

%t Table[prd = Product[Binomial[n, k], {k, 0, n}]; If[prd == 1, 0, Length[FactorInteger[prd]]], {n, 0, 100}] (* _T. D. Noe_, Mar 21 2013 *)

%o (PARI) a(n) = {sfp = Set(); for (k=1, n-1, sfp = setunion(sfp, Set(factor(binomial(n, k))[,1]))); return (length(sfp));} \\ _Michel Marcus_, Mar 21 2013

%o (Haskell)

%o a004788 = a001221 . a001142  -- _Reinhard Zumkeller_, Mar 16 2015

%Y Cf. A004789.

%Y Cf. A001221, A001142, A256113.

%K nonn

%O 0,5

%A _Clark Kimberling_