A084694 Squarefree numbers which are products of three consecutive numbers. I.e., squarefree numbers of the form k^3 - k.

6, 210, 2730, 10626, 26970, 39270, 54834, 74046, 195054, 287430, 342930, 474474, 635970, 830490, 1061106, 1190910, 1330890, 1481430, 2196870, 2627934, 2863146, 3944154, 4574130, 5639574, 6028386, 6434670, 7301190, 8242206, 9260790

Offset: 1

Author

Amarnath Murthy, Jun 04 2003

Keywords

• nonn

Comments

No product of 4 consecutive numbers is squarefree.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A007531, A007675.

Programs

Mathematica

f[n_] := n*(n + 1)*(n + 2); f /@ Select[Range[250], AllTrue[# + {0, 1, 2}, SquareFreeQ] &] (* Amiram Eldar, Feb 25 2021 *)

PARI

lista(nn) = {for (k=1, nn, if (issquarefree(x=k^3-k), print1(x, ", ")););} \\ Michel Marcus, Jul 29 2017

Formula

a(n) = A007531(A007675(n)+2). - Amiram Eldar, Feb 25 2021

Extensions

Offset corrected to 1 by Michel Marcus, Jul 29 2017