A206547 Positive odd numbers relatively prime to 21.

1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 95, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 131, 137, 139, 143, 145, 149, 151, 155, 157, 163, 167, 169, 173, 179, 181, 185, 187, 191, 193, 197, 199, 205, 209, 211

Offset

1,2

Comments

These are the positive integers not divisible by 2, 3, or 7.

Numbers coprime to 42. The asymptotic density of this sequence is 2/7. - Amiram Eldar, Oct 23 2020

Links

Table of n, a(n) for n=1..61.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n) = a(n-12) + 42, n>=13.

a(n) = a(n-1) + a(n-12) - a(n-13), n>=13, with a(0)=-1.

a(n) = 2*n-1 + 2*sum(F21[j]*floor((n+(j-1))/12),j=1..12), with F21=[1,2,0,1,0,1,0,1,0,2,1,0], n>=1. For n=0 this becomes -1, but the following o.g.f. has a(0)=0 if it starts with x^0.

O.g.f.: x*(1+x^12+4*x*(1+x^10)+6*x^2*(1+x^8)+2*x^3*(1+x^6)+4*x^4*(1+x^4)+2*x^5*(1+x^2)+4*x^6)/((1-x^12)*(1-x)). The denominator could be factored into cyclotomic polynomials. Compare with the formula contribution from R. J. Mathar in A007775.

Mathematica

Select[Range[1, 211, 2], CoprimeQ[#, 21]&] (* Harvey P. Dale, Jul 28 2020 *)

Crossrefs

Cf. A007775, A204458.

Sequence in context: A093685 A337658 A206548 * A295584 A185208 A216227

Adjacent sequences: A206544 A206545 A206546 * A206548 A206549 A206550

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 10 2012

Status

approved