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Numbers n such that central binomial coefficient C(n, floor(n/2)) is squarefree.
19

%I #26 Jul 10 2022 09:42:40

%S 0,1,2,3,4,5,7,8,11,17,19,23,71

%N Numbers n such that central binomial coefficient C(n, floor(n/2)) is squarefree.

%C No other n < 10^8. - _T. D. Noe_, Apr 06 2007

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%t Select[Range[0, 100], SquareFreeQ[Binomial[#,Floor[#/2]]]&] (* _Harvey P. Dale_, Mar 11 2011 *)

%o (PARI) is(n)=issquarefree(binomial(n,n\2)) \\ _Charles R Greathouse IV_, Jul 16 2011

%Y Cf. A001405.

%Y Cf. A056651 (cubefree central binomial coefficients).

%K nonn,hard

%O 1,3

%A _Eric W. Weisstein_

%E 0 added by _T. D. Noe_, Mar 06 2014