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

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A005117, A065474, A117204, A117205.

Sequence in context: A232011 A153183 A247648 * A081118 A363583 A355918

Adjacent sequences: A117200 A117201 A117202 * A117204 A117205 A117206

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