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

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

Offset: 0

Author

T. D. Noe, Mar 05 2014

Keywords

• nonn

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..5000

Crossrefs

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

Programs

Maple

A238337 := proc(n)
    local sqf ;
    sqf := {} ;
    for k from 0 to n do
        b := binomial(n,k) ;
        if b=1 or numtheory[issqrfree](b) then
            sqf := sqf union { b} ;
        end if;
    end do:
    nops(sqf) ;
end proc:
seq(A238337(n),n=0..10) ; # R. J. Mathar, Mar 06 2014

Mathematica

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

Formula

a(n) + A064460(n) = A008619(n). - R. J. Mathar, Jan 18 2018