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

%I A238337 #13 Jan 18 2018 08:55:18
%S A238337 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 A238337 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 A238337 2,3,4,4,8,6,9,1,4,9,2,3,7,9,17,1,1,2,3,2
%N A238337 Number of distinct squarefree numbers in row n of Pascal's triangle.
%H A238337 T. D. Noe, <a href="/A238337/b238337.txt">Table of n, a(n) for n = 0..5000</a>
%F A238337 a(n) + A064460(n) = A008619(n). - _R. J. Mathar_, Jan 18 2018
%e A238337 a(10)=3 because in row 10 of A007318 we observe the three squarefree numbers 1, 10 and 210.
%p A238337 A238337 := proc(n)
%p A238337     local sqf ;
%p A238337     sqf := {} ;
%p A238337     for k from 0 to n do
%p A238337         b := binomial(n,k) ;
%p A238337         if b=1 or numtheory[issqrfree](b) then
%p A238337             sqf := sqf union { b} ;
%p A238337         end if;
%p A238337     end do:
%p A238337     nops(sqf) ;
%p A238337 end proc:
%p A238337 seq(A238337(n),n=0..10) ; # _R. J. Mathar_, Mar 06 2014
%t A238337 Table[Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]], {n, 0, 100}]
%Y A238337 Cf. A048276 (number of squarefree numbers in the entire row), A238336.
%K A238337 nonn
%O A238337 0,3
%A A238337 _T. D. Noe_, Mar 05 2014