A274546 Numbers m such that 5*m is squarefree.

1, 2, 3, 6, 7, 11, 13, 14, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 66, 67, 69, 71, 73, 74, 77, 78, 79, 82, 83, 86, 87, 89, 91, 93, 94, 97, 101, 102, 103, 106, 107, 109, 111, 113, 114, 118, 119, 122, 123, 127, 129, 131, 133, 134

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 05 2016

Keywords

• nonn
• easy

Comments

Squarefree numbers coprime to 5.

Examples

			6 is in this sequence because 5*6 = 30 = 2*3*5 is squarefree.
		

Links

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

Crossrefs

Numbers m such that m*A005117(k) is squarefree: A005117 (k = 1), A056911 (k = 2), A261034 (k = 3), this sequence (k = 5), A276378 (k = 6).

Cf. A008587.

Programs

Magma

[n: n in [1..135] | IsSquarefree(5*n)];

Mathematica

Select[Range[135], !Divisible[#, 5] && SquareFreeQ[#] &] (* Amiram Eldar, Sep 26 2023 *)

PARI

lista(nn) = for(n=1, nn, if(issquarefree(5*n), print1(n, ", "))); \\ Altug Alkan, Sep 05 2016

PARI

is(n)=n%5 && issquarefree(n) \\ Charles R Greathouse IV, Sep 06 2016

Formula

a(n) ~ Pi^2*n/5. - Charles R Greathouse IV, Sep 06 2016 [corrected by Amiram Eldar, Sep 26 2023]

Sum_{n>=1} 1/a(n)^s = (5^s)*zeta(s)/((1+5^s)*zeta(2*s)), s>1. - Amiram Eldar, Sep 26 2023