This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117206 #15 Feb 17 2021 03:59:58
%S A117206 1,2,3,6,7,10,11,15,17,19,21,22,26,29,30,31,33,34,35,37,39,42,43,46,
%T A117206 47,51,53,55,57,58,62,65,66,67,69,70,71,73,78,79,82,83,87,89,91,93,94,
%U A117206 97,101,102,103,105,106,107,109,110,111,114,115,118,119,127,129,130,133
%N A117206 Squarefree positive integers k such that 2*k-1 is also squarefree.
%C A117206 The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987). - _Amiram Eldar_, Feb 17 2021
%H A117206 Amiram Eldar, <a href="/A117206/b117206.txt">Table of n, a(n) for n = 1..10000</a>
%H A117206 Paul Erdős and Aleksandar Ivić, <a href="https://users.renyi.hu/~p_erdos/1987-32b.pdf">The distribution of values of a certain class of arithmetic functions at consecutive integers</a>, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 45-91.
%F A117206 a(n) = (A117205(n) + 1)/2.
%e A117206 10 and 2*10 - 1 = 19 are both squarefree, so 10 is in the sequence.
%p A117206 with(numtheory): a:=proc(n) if abs(mobius(n))>0 and abs(mobius(2*n-1))>0 then n else fi end: seq(a(n),n=1..160); # _Emeric Deutsch_, Mar 08 2006
%t A117206 Select[Range[200],And@@SquareFreeQ/@{#,2#-1}&] (* _Harvey P. Dale_, Dec 17 2012 *)
%Y A117206 Cf. A005117, A065474, A117204, A117205.
%K A117206 nonn
%O A117206 1,2
%A A117206 _Leroy Quet_, Mar 02 2006
%E A117206 More terms from _Emeric Deutsch_, Mar 08 2006