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A272799 Numbers n such that 2n - 1 and 2n + 1 are squarefree. 3

%I

%S 1,2,3,6,7,8,9,10,11,15,16,17,18,19,20,21,26,27,28,29,30,33,34,35,36,

%T 39,42,43,44,45,46,47,48,51,52,53,54,55,56,57,64,65,66,69,70,71,72,75,

%U 78,79,80,81,82,83,89,90,91,92,93,96,97,98,99,100,101,102,105,106,107,108,109,110

%N Numbers n such that 2n - 1 and 2n + 1 are squarefree.

%H Robert Israel, <a href="/A272799/b272799.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A069977(n)+1)/2. - _Charles R Greathouse IV_, May 15 2016

%e a(1) = 1 because 2*1 - 1 = 1 is squarefree and 2*1 + 1 = 3 is squarefree.

%p Res:= NULL: count:= 0: state:= 1;

%p for n from 1 while count < 100 do

%p if numtheory:-issqrfree(2*n+1) then

%p if state = 1 then Res:= Res, n; count:= count+1;

%p else

%p state:= 1;

%p fi

%p else

%p state:= 0;

%p fi

%p od:

%p Res; # _Robert Israel_, Apr 15 2019

%t Select[Range[12^4], And[Or[# == 1, GCD @@ FactorInteger[#][[All, 2]] > 1], SquareFreeQ[# - 1], SquareFreeQ[# + 1]] &] (* _Michael De Vlieger_, May 08 2016 *)

%o (MAGMA) [n: n in [1..110] | IsSquarefree(2*n-1) and IsSquarefree(2*n+1)];

%o (PARI) is(n)=issquarefree(2*n-1) && issquarefree(2*n+1) \\ _Charles R Greathouse IV_, May 15 2016

%Y Cf. A069977, A226993.

%K nonn,easy

%O 1,2

%A _Juri-Stepan Gerasimov_, May 06 2016

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Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)