A119356 Numbers k such that A000330(k) is squarefree.

1, 2, 3, 4, 5, 6, 9, 10, 11, 14, 17, 18, 19, 20, 21, 22, 28, 29, 30, 33, 34, 35, 36, 38, 41, 42, 43, 44, 45, 46, 51, 52, 57, 58, 59, 61, 65, 66, 68, 69, 70, 76, 77, 78, 82, 83, 85, 86, 89, 90, 91, 92, 93, 101, 102, 105, 106, 109, 110, 113, 114, 115, 116, 117, 118, 123, 126

Offset: 1

Author

Zak Seidov, May 16 2006

Keywords

• nonn

Comments

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 8, 53, 504, 5029, 50187, 501925, 5019527, 50194688, 501948054, 5019478733, ... . Conjecture: The asymptotic density of this sequence is 4 * Product_{p prime} (1 - 3/p^2) = 4 * A206256 = 0.50194792... . - Amiram Eldar, Sep 24 2024

Examples

			10 is a term because 10*11*(2*10+1)/6 = 5*7*11 is squarefree.
		

Links

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

Crossrefs

Cf. A000330, A005117, A172186 (subsequence), A206256,

Programs

Maple

filter:= n -> numtheory:-issqrfree(n*(n+1)*(2*n+1)/6):
select(filter, [$1..200]); # Robert Israel, Aug 04 2020

Mathematica

Select[Range[126],SquareFreeQ[#(#+1)(2#+1)/6]&] (* James C. McMahon, Sep 15 2024 *)

PARI

lista(nn) = {for (n=1, nn, if (issquarefree(n*(n+1)*(2*n+1)/6), print1(n, ", ")););} \\ Michel Marcus, May 18 2013