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A238337 Number of distinct squarefree numbers in row n of Pascal's triangle. 6

%I

%S 1,1,2,2,2,3,3,4,2,1,3,6,2,5,6,7,1,3,1,4,4,5,6,12,2,2,4,1,2,6,3,6,1,2,

%T 4,4,1,4,7,6,2,6,7,13,8,4,10,21,1,1,1,2,3,9,2,3,1,3,5,11,4,13,20,4,1,

%U 2,3,4,4,8,6,9,1,4,9,2,3,7,9,17,1,1,2,3,2

%N Number of distinct squarefree numbers in row n of Pascal's triangle.

%H T. D. Noe, <a href="/A238337/b238337.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) + A064460(n) = A008619(n). - _R. J. Mathar_, Jan 18 2018

%e a(10)=3 because in row 10 of A007318 we observe the three squarefree numbers 1, 10 and 210.

%p A238337 := proc(n)

%p local sqf ;

%p sqf := {} ;

%p for k from 0 to n do

%p b := binomial(n,k) ;

%p if b=1 or numtheory[issqrfree](b) then

%p sqf := sqf union { b} ;

%p end if;

%p end do:

%p nops(sqf) ;

%p end proc:

%p seq(A238337(n),n=0..10) ; # _R. J. Mathar_, Mar 06 2014

%t Table[Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]], {n, 0, 100}]

%Y Cf. A048276 (number of squarefree numbers in the entire row), A238336.

%K nonn

%O 0,3

%A _T. D. Noe_, Mar 05 2014

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Last modified September 16 06:38 EDT 2019. Contains 327090 sequences. (Running on oeis4.)