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

1,2

Comments

Conjectured to be finite.

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

Links

Table of n, a(n) for n=1..11.

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 *)

Prog

(Magma) [n: n in [1..200] | IsSquarefree(n) and IsSquarefree(Binomial(2^n-1, n))];
(PARI) is(n)=issquarefree(n) && issquarefree(binomial(2^n-1, n)) \\ Charles R Greathouse IV, Nov 16 2014

Crossrefs

Cf. A000225, A005117, A136556.

Sequence in context: A030037 A077078 A077079 * A079969 A034064 A034074

Adjacent sequences: A246696 A246697 A246698 * A246700 A246701 A246702

Keyword

nonn,changed

Author

Juri-Stepan Gerasimov, Nov 15 2014

Status

approved