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

1,2

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A007674, A172187, A179017, A206256.

Sequence in context: A348565 A316946 A005984 * A355942 A178761 A274037

Adjacent sequences: A172183 A172184 A172185 * A172187 A172188 A172189

Keyword

nonn

Author

Artur Jasinski, Jan 28 2010

Status

approved