A124569 Numbers k such that k, k+2, k+4 and k+6 are squarefree.

1, 11, 13, 15, 17, 29, 31, 33, 35, 37, 51, 53, 55, 65, 67, 83, 85, 87, 89, 91, 101, 103, 105, 107, 109, 127, 137, 139, 155, 157, 159, 161, 177, 179, 181, 191, 193, 195, 197, 199, 209, 211, 213, 215, 217, 227, 229, 231, 233, 235, 247, 249, 251, 253, 263, 265, 267

Offset: 1

Author

Zak Seidov, Dec 27 2006

Keywords

• nonn

Comments

Numbers k, k+2, k+4 and k+6 are four successive odd squarefree numbers.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007675, A024556.

Programs

Maple

filter:= proc(n) andmap(numtheory:-issqrfree,[n,n+2,n+4,n+6]) end proc:
select(filter, [seq(i,i=1..1000,2)]); # Robert Israel, Jun 08 2021

Mathematica

okQ[n_] := AllTrue[n + {0, 2, 4, 6}, SquareFreeQ];
Select[Range[1, 1000, 2], okQ] (* Jean-François Alcover, May 18 2023 *)

PARI

isok(n) = issquarefree(n) && issquarefree(n+2) && issquarefree(n+4) && issquarefree(n+6); \\ Michel Marcus, Oct 11 2013