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

%I

%S 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 87,93,95,103,107,111,115,119,123,131,133,139,141,143,149,155,157,159,

%U 165,167,173,179,183,187,191,195,203,205,211,213,215,219,221,223,227

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

%C a(n) = 2*A117204(n) + 1.

%e 21 and (21-1)/2 = 10 are both squarefree, so 21 is in the sequence.

%p 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 fQ[n_] := Max @@ Last /@ FactorInteger@n < 2; Select[ 2Range@113 + 1, fQ@# && fQ[(# - 1)/2] &] (* _Robert G. Wilson v_, Apr 18 2006 *)

%o (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 Cf. A005117, A117204, A117205.

%K nonn

%O 1,1

%A _Leroy Quet_, Mar 02 2006

%E More terms from _Emeric Deutsch_ and _Reinhard Zumkeller_, Mar 07 2006

%E More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 23 2006

%E More terms from _Robert G. Wilson v_, Apr 18 2006

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)