OFFSET
1,2
COMMENTS
These are the numbers from A005117 that are not divisible by 2 and 3.
Squarefree numbers coprime to 6. - Robert Israel, Sep 02 2016
The asymptotic density of this sequence is 3/Pi^2 (A104141). - Amiram Eldar, May 22 2020
From Peter Munn, Nov 20 2020: (Start)
The products generated from each subset of A215848 (primes greater than 3).
Closed under the commutative binary operation A059897(.,.), forming a subgroup of the positive integers under A059897. (End)
Multiplied by 6 we have 6, 30, 42, 66, 78, 102, ..., the values that may appear in A076978 after the 1, 2. [Don Reble, Dec 02 2020] - R. J. Mathar, Dec 15 2020
By the von Staudt-Clausen theorem, denominators of Bernoulli numbers are of the form 6*a(n) for some n. - Charles R Greathouse IV, May 16 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
{a(n) : n >= 1} = {A003961(A003961(A005117(n))) : n >= 1} = {A003961(A056911(n))) : n >= 1}. - Peter Munn, Nov 20 2020
Sum_{n>=1} 1/a(n)^s = (6^s)*zeta(s)/((1+2^s)*(1+3^s)*zeta(2*s)), s>1. - Amiram Eldar, Sep 26 2023
EXAMPLE
5 is in this sequence because 6*5 = 30 = 2*3*5 is squarefree.
MAPLE
select(numtheory:-issqrfree, [seq(seq(6*i+j, j=[1, 5]), i=0..100)]); # Robert Israel, Sep 02 2016
MATHEMATICA
Select[Range@ 212, SquareFreeQ[6 #] &] (* Michael De Vlieger, Sep 02 2016 *)
PROG
(Magma) [n: n in [1..230] | IsSquarefree(6*n)];
(PARI) is(n) = issquarefree(6*n) \\ Felix Fröhlich, Sep 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, Sep 02 2016
STATUS
approved