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A238337
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Number of distinct squarefree numbers in row n of Pascal's triangle.
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6
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(10)=3 because in row 10 of A007318 we observe the three squarefree numbers 1, 10 and 210.
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MAPLE
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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:
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MATHEMATICA
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Table[Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]], {n, 0, 100}]
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CROSSREFS
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Cf. A048276 (number of squarefree numbers in the entire row), A238336.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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