A117206 Squarefree positive integers k such that 2*k-1 is also squarefree.

1, 2, 3, 6, 7, 10, 11, 15, 17, 19, 21, 22, 26, 29, 30, 31, 33, 34, 35, 37, 39, 42, 43, 46, 47, 51, 53, 55, 57, 58, 62, 65, 66, 67, 69, 70, 71, 73, 78, 79, 82, 83, 87, 89, 91, 93, 94, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 114, 115, 118, 119, 127, 129, 130, 133

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, Feb 17 2021

Examples

			10 and 2*10 - 1 = 19 are both squarefree, so 10 is in the sequence.
		

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.

Crossrefs

Cf. A005117, A065474, A117204, A117205.

Programs

Maple

with(numtheory): a:=proc(n) if abs(mobius(n))>0 and abs(mobius(2*n-1))>0 then n else fi end: seq(a(n),n=1..160); # Emeric Deutsch, Mar 08 2006

Mathematica

Select[Range[200],And@@SquareFreeQ/@{#,2#-1}&] (* Harvey P. Dale, Dec 17 2012 *)

Formula

a(n) = (A117205(n) + 1)/2.

Extensions

More terms from Emeric Deutsch, Mar 08 2006