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 A117205 #16 Feb 17 2021 04:01:05
%S A117205 1,3,5,11,13,19,21,29,33,37,41,43,51,57,59,61,65,67,69,73,77,83,85,91,
%T A117205 93,101,105,109,113,115,123,129,131,133,137,139,141,145,155,157,163,
%U A117205 165,173,177,181,185,187,193,201,203,205,209,211,213,217,219,221,227,229
%N A117205 Odd squarefree positive integers k such that (k+1)/2 is also squarefree.
%C A117205 The asymptotic density of this sequence is (3/4)*A065474 = 0.2419755742... (Erdős and Ivić, 1987). - _Amiram Eldar_, Feb 17 2021
%H A117205 Amiram Eldar, <a href="/A117205/b117205.txt">Table of n, a(n) for n = 1..10000</a>
%H A117205 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 A117205 a(n) = 2 * A117206(n) - 1.
%e A117205 21 and (21+1)/2 = 11 are both squarefree, so 21 is in the sequence.
%p A117205 with(numtheory): a:=proc(n) if n mod 2 =1 and abs(mobius(n))>0 and abs(mobius((n+1)/2))>0 then n else fi end: seq(a(n),n=1..300); # _Emeric Deutsch_, Mar 07 2006
%t A117205 Select[Range[1,301,2],And@@(SquareFreeQ/@{#,(#+1)/2})&] (* _Harvey P. Dale_, Jul 30 2013 *)
%Y A117205 Cf. A005117, A065474, A117203, A117206.
%K A117205 nonn
%O A117205 1,2
%A A117205 _Leroy Quet_, Mar 02 2006
%E A117205 More terms from _Emeric Deutsch_, Mar 07 2006