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

1,2

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A168009 A134697 A032975 * A137582 A116965 A356007

Adjacent sequences: A119353 A119354 A119355 * A119357 A119358 A119359

Keyword

nonn

Author

Zak Seidov, May 16 2006

Status

approved