A261034 Numbers m such that 3*m is squarefree.

1, 2, 5, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 34, 35, 37, 38, 41, 43, 46, 47, 53, 55, 58, 59, 61, 62, 65, 67, 70, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 91, 94, 95, 97, 101, 103, 106, 107, 109, 110, 113, 115, 118, 119, 122, 127, 130, 131

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 07 2015

Keywords

• nonn
• easy

Comments

These are the numbers from A005117 that are not divisible by 3. See the Maple program by Robert Israel. - Wolfdieter Lang, Aug 21 2015

Squarefree numbers divisible by 3: 3, 6, 15, 21, 30, 33, 39, 42, 51, 57, 66, 69, 78, 87, 93, 102, ...

Examples

			10 is in this sequence because 3*10 = 30 is squarefree.
		

Crossrefs

Cf. A045344, A088245.

Numbers m such that k*m is squarefree: A005117 (k = 1), A056911 (k = 2), this sequence (k = 3), A274546 (k = 5), A276378 (k = 6).

Programs

Magma

[n: n in [1..200] | IsSquarefree(3*n)];

Maple

select(numtheory:-issqrfree, [seq(seq(3*i+j,j=1..2),i=0..1000)]); # Robert Israel, Aug 07 2015

Mathematica

Select[Range[0, 200], SquareFreeQ[3 #] &] (* Vincenzo Librandi, Aug 08 2015 *)

PARI

is(n)=n%3 && issquarefree(n) \\ Charles R Greathouse IV, Aug 07 2015

Formula

a(n) ~ 2*Pi^2*n/9. - Charles R Greathouse IV, Aug 07 2015

Sum_{n>=1} 1/a(n)^s = (3^s)*zeta(s)/((1+3^s)*zeta(2*s)), s>1. - Amiram Eldar, Sep 26 2023

Extensions

Corrected and extended by Vincenzo Librandi, Aug 08 2015