A172186 Numbers k such that k, k+1 and 2*k+1 are squarefree.

1, 2, 5, 6, 10, 14, 21, 29, 30, 33, 34, 38, 41, 42, 46, 57, 61, 65, 66, 69, 70, 77, 78, 82, 86, 93, 101, 102, 105, 106, 109, 110, 113, 114, 118, 129, 133, 138, 141, 142, 145, 154, 158, 165, 173, 177, 178, 182, 185, 186, 190, 194, 201, 205, 209, 210, 213, 214, 217, 218

Offset: 1

Author

Artur Jasinski, Jan 28 2010

Keywords

• nonn

Comments

This sequence is similar to A007674. For terms in A007674 which lack in this sequence see A172187.

The asymptotic density of this sequence is 2 * Product_{p prime} (1 - 3/p^2) = 2 * A206256 = 0.250973961811... (Tsang, 1985). - Amiram Eldar, Feb 26 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Kai-Man Tsang, The distribution of r-tuples of square-free numbers, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.

Crossrefs

Cf. A007674, A172187, A179017, A206256.

Programs

Mathematica

Select[Range[250], And @@ SquareFreeQ /@ {#, # + 1, 2 # + 1} &]  (* Harvey P. Dale, Mar 11 2011 *)

Formula

a(n) = (A179017(n)-1)/2.