This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A206547 #17 Oct 23 2020 06:18:32 %S A206547 1,5,11,13,17,19,23,25,29,31,37,41,43,47,53,55,59,61,65,67,71,73,79, %T A206547 83,85,89,95,97,101,103,107,109,113,115,121,125,127,131,137,139,143, %U A206547 145,149,151,155,157,163,167,169,173,179,181,185,187,191,193,197,199,205,209,211 %N A206547 Positive odd numbers relatively prime to 21. %C A206547 These are the positive integers not divisible by 2, 3, or 7. %C A206547 Numbers coprime to 42. The asymptotic density of this sequence is 2/7. - _Amiram Eldar_, Oct 23 2020 %H A206547 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1). %F A206547 a(n) = a(n-12) + 42, n>=13. %F A206547 a(n) = a(n-1) + a(n-12) - a(n-13), n>=13, with a(0)=-1. %F A206547 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. %F A206547 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. %t A206547 Select[Range[1,211,2],CoprimeQ[#,21]&] (* _Harvey P. Dale_, Jul 28 2020 *) %Y A206547 Cf. A007775, A204458. %K A206547 nonn,easy %O A206547 1,2 %A A206547 _Wolfdieter Lang_, Feb 10 2012