A117204 Squarefree positive integers k such that 2*k+1 is also squarefree.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 17, 19, 21, 23, 26, 29, 30, 33, 34, 35, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 59, 61, 65, 66, 69, 70, 71, 74, 77, 78, 79, 82, 83, 86, 89, 91, 93, 95, 97, 101, 102, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119

Offset: 1

Author

Leroy Quet, Mar 02 2006

Keywords

• nonn

Comments

The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987). - Amiram Eldar, Mar 02 2021

Examples

			10 and 2*10 +1 = 21 are both squarefree, so 10 is in the sequence.
		

Links

• Ivan Neretin, 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.

Crossrefs

Cf. A005117, A117203, A117206.

Cf. A005384, A111153, A065474.

Programs

Mathematica

sfQ[n_]:=SquareFreeQ[n]&&SquareFreeQ[2n+1]; Select [Range[200],sfQ] (* Harvey P. Dale, Mar 12 2011 *)

Formula

a(n) = (A117203(n) - 1)/2.

Extensions

More terms from Jonathan Vos Post, Mar 03 2006

Corrected and extended by Harvey P. Dale, Mar 12 2011