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A117203
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Odd squarefree positive integers k such that (k-1)/2 is also squarefree.
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3
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3, 5, 7, 11, 13, 15, 21, 23, 29, 31, 35, 39, 43, 47, 53, 59, 61, 67, 69, 71, 77, 79, 83, 85, 87, 93, 95, 103, 107, 111, 115, 119, 123, 131, 133, 139, 141, 143, 149, 155, 157, 159, 165, 167, 173, 179, 183, 187, 191, 195, 203, 205, 211, 213, 215, 219, 221, 223, 227
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is (3/4)*A065474 = 0.2419755742... (Erdős and Ivić, 1987). - Amiram Eldar, Feb 17 2021
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LINKS
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FORMULA
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EXAMPLE
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21 and (21-1)/2 = 10 are both squarefree, so 21 is in the sequence.
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MAPLE
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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
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MATHEMATICA
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fQ[n_] := Max @@ Last /@ FactorInteger@n < 2; Select[ 2Range@113 + 1, fQ@# && fQ[(# - 1)/2] &] (* Robert G. Wilson v, Apr 18 2006 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 23 2006
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STATUS
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approved
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