A246699 Squarefree n such that C(2^n - 1, n) is also squarefree, where C is the binomial coefficient.

1, 2, 3, 6, 11, 21, 29, 31, 51, 55, 57

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 15 2014

Keywords

• nonn

Comments

Conjectured to be finite.

The subsequence of squarefree numbers in A245569. - M. F. Hasler, Nov 28 2014

Crossrefs

Cf. A000225, A005117, A136556.

Programs

Magma

[n: n in [1..200] | IsSquarefree(n) and IsSquarefree(Binomial(2^n-1, n))];

Mathematica

Select[Range[100], SquareFreeQ[#] && SquareFreeQ[Binomial[2^# - 1, #]] &] (* Vincenzo Librandi, Nov 14 2014 *)
Select[Range[60],AllTrue[{#,Binomial[2^#-1,#]},SquareFreeQ]&] (* Harvey P. Dale, Feb 07 2025 *)

PARI

is(n)=issquarefree(n) && issquarefree(binomial(2^n-1,n)) \\ Charles R Greathouse IV, Nov 16 2014