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A117203 Odd squarefree positive integers k such that (k-1)/2 is also squarefree.

%I A117203 #26 Feb 17 2021 04:06:27
%S A117203 3,5,7,11,13,15,21,23,29,31,35,39,43,47,53,59,61,67,69,71,77,79,83,85,
%T A117203 87,93,95,103,107,111,115,119,123,131,133,139,141,143,149,155,157,159,
%U A117203 165,167,173,179,183,187,191,195,203,205,211,213,215,219,221,223,227
%N A117203 Odd squarefree positive integers k such that (k-1)/2 is also squarefree.
%C A117203 The asymptotic density of this sequence is (3/4)*A065474 = 0.2419755742... (Erdős and Ivić, 1987). - _Amiram Eldar_, Feb 17 2021
%H A117203 Amiram Eldar, <a href="/A117203/b117203.txt">Table of n, a(n) for n = 1..10000</a>
%H A117203 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 A117203 a(n) = 2*A117204(n) + 1.
%e A117203 21 and (21-1)/2 = 10 are both squarefree, so 21 is in the sequence.
%p A117203 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=2..300); # _Emeric Deutsch_, Mar 07 2006
%t A117203 fQ[n_] := Max @@ Last /@ FactorInteger@n < 2; Select[ 2Range@113 + 1, fQ@# && fQ[(# - 1)/2] &] (* _Robert G. Wilson v_, Apr 18 2006 *)
%o A117203 (PARI) for (i=1,100,if(issquarefree(2*i+1) && issquarefree(i),print1(2*i+1,","))) \\ Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 23 2006
%Y A117203 Cf. A005117, A065474, A117204, A117205.
%K A117203 nonn
%O A117203 1,1
%A A117203 _Leroy Quet_, Mar 02 2006
%E A117203 More terms from _Emeric Deutsch_ and _Reinhard Zumkeller_, Mar 07 2006
%E A117203 More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 23 2006
%E A117203 More terms from _Robert G. Wilson v_, Apr 18 2006