A358428 Numbers k such that k^2 + 1, k^2 + 2 and k^2 + 3 are all squarefree.

2, 6, 8, 10, 16, 20, 26, 28, 30, 34, 36, 42, 44, 46, 48, 52, 54, 56, 60, 62, 64, 66, 72, 74, 78, 80, 84, 88, 90, 92, 96, 98, 100, 106, 108, 114, 116, 120, 126, 128, 134, 136, 138, 142, 144, 146, 150, 152, 154, 156, 160, 162, 164, 170, 172, 174, 178, 180, 186, 188, 190, 192, 196, 198, 200

Offset: 1

Author

Michel Marcus, Nov 15 2022

Keywords

• nonn

Comments

Wongcharoenbhorn proves that this sequence is infinite and gives an infinite product for its density; its value is about 0.313992945491, so a(n) ~ kn with k around 3.18478492705. - Charles R Greathouse IV, Dec 11 2022

Links

• W. Wongcharoenbhorn, Three consecutive near-square squarefree numbers, arXiv:2211.07237 [math.NT], 2022.

Crossrefs

Subsequence of A335962.

Programs

Mathematica

Select[Range[200], And @@ SquareFreeQ /@ (#^2 + {1, 2, 3}) &] (* Amiram Eldar, Nov 15 2022 *)

PARI

isok(k) = issquarefree(k^2+1) && issquarefree(k^2+2) && issquarefree(k^2+3);