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A117203 Odd squarefree positive integers k such that (k-1)/2 is also squarefree. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is (3/4)*A065474 = 0.2419755742... (Erdős and Ivić, 1987). - Amiram Eldar, Feb 17 2021
LINKS
Paul Erdős and Aleksandar Ivić, The distribution of values of a certain class of arithmetic functions at consecutive integers, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 45-91.
FORMULA
a(n) = 2*A117204(n) + 1.
EXAMPLE
21 and (21-1)/2 = 10 are both squarefree, so 21 is in the sequence.
MAPLE
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
MATHEMATICA
fQ[n_] := Max @@ Last /@ FactorInteger@n < 2; Select[ 2Range@113 + 1, fQ@# && fQ[(# - 1)/2] &] (* Robert G. Wilson v, Apr 18 2006 *)
PROG
(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
CROSSREFS
Sequence in context: A232011 A153183 A247648 * A081118 A363583 A355918
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 02 2006
EXTENSIONS
More terms from Emeric Deutsch and Reinhard Zumkeller, Mar 07 2006
More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 23 2006
More terms from Robert G. Wilson v, Apr 18 2006
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)