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

1,1

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

Table of n, a(n) for n=1..65.

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A335962.

Sequence in context: A296387 A302658 A324175 * A084909 A038619 A118257

Adjacent sequences: A358425 A358426 A358427 * A358429 A358430 A358431

Keyword

nonn

Author

Michel Marcus, Nov 15 2022

Status

approved