|
%I #13 Jan 18 2018 08:55:22
%S 0,0,0,0,1,0,1,0,3,4,3,0,5,2,2,1,8,6,9,6,7,6,6,0,11,11,10,13,13,9,13,
%T 10,16,15,14,14,18,15,13,14,19,15,15,9,15,19,14,3,24,24,25,24,24,18,
%U 26,25,28,26,25,19,27,18,12,28,32,31,31,30,31,27,30,27,36
%N Number of distinct nonsquarefree entries in n-th row of Pascal's triangle.
%H T. D. Noe, <a href="/A064460/b064460.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) + A238337(n) = A008619(n). - _R. J. Mathar_, Jan 18 2018
%e a(13) = 2 because C(13,5) = 3^2*11*13 and C(13,6) = 2^2*3*11*13.
%t f[ n_ ] := (c = 0; k = 1; While[ k < n/2 + .5, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Table[ f[ n ], {n, 0, 100} ]
%o (PARI) a(n) = sum(k=0, n\2, !issquarefree(binomial(n, k))); \\ _Michel Marcus_, Mar 05 2014
%Y Cf. A048277, A064461, A064462.
%K easy,nonn
%O 0,9
%A _Robert G. Wilson v_, Oct 02 2001
|
