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 A216913 #27 Nov 17 2022 05:14:59
%S A216913 1,2,1,2,5,2,7,2,1,10,11,2,13,14,5,2,17,2,19,10,7,22,23,2,5,26,1,14,
%T A216913 29,10,31,2,11,34,35,2,37,38,13,10,41,14,43,22,5,46,47,2,7,10,17,26,
%U A216913 53,2,55,14,19,58,59,10,61,62,7,2,65,22,67,34,23,70,71
%N A216913 a(n) = Gauss_primorial(3*n, 3) / Gauss_primorial(3*n, 3*n).
%C A216913 The term Gauss primorial was introduced in A216914 and denotes the restriction of the Gauss factorial N_n! (see A216919) to prime factors.
%C A216913 Multiplicative because both A007947 and A109007 are. - _Andrew Howroyd_, Aug 02 2018
%H A216913 Andrew Howroyd, <a href="/A216913/b216913.txt">Table of n, a(n) for n = 1..1000</a>
%F A216913 a(n) = n/Sum_{k=1..3n} floor(cos^2(Pi*k^(3n)/(3n))). - _Anthony Browne_, May 24 2016
%F A216913 a(n) = A007947(n)/A109007(n). - _Andrew Howroyd_, Aug 02 2018
%F A216913 a(n) = Sum_{d|n} phi(d)*mu(3d)^2. - _Ridouane Oudra_, Oct 19 2019
%F A216913 From _Amiram Eldar_, Nov 17 2022: (Start)
%F A216913 Multiplicative with a(3^e) = 1, and a(p^e) = p for p != 3.
%F A216913 Sum_{k=1..n} a(k) ~ c * n^2, where c = (9/22) * Product_{p prime} (1 - 1/(p*(p+1))) = (9/22) * A065463 = 0.2881809... . (End)
%t A216913 Table[n/Sum[Floor[Cos[Pi k^(3 n)/(3 n)]^2], {k, 3 n}], {n, 71}] (* _Michael De Vlieger_, May 24 2016 *)
%t A216913 a[n_] := Times @@ (First /@ FactorInteger[n])/GCD[n, 3]; Array[a, 100] (* _Amiram Eldar_, Nov 17 2022 *)
%o A216913 (PARI) a(n)={factorback(factor(n)[, 1])/gcd(3,n)} \\ _Andrew Howroyd_, Aug 02 2018
%o A216913 (Sage)
%o A216913 def Gauss_primorial(N, n):
%o A216913 return mul(j for j in (1..N) if gcd(j, n) == 1 and is_prime(j))
%o A216913 def A216913(n): return Gauss_primorial(3*n, 3)/Gauss_primorial(3*n, 3*n)
%o A216913 [A216913(n) for n in (1..80)]
%o A216913 (Magma) [&+[EulerPhi(d)*MoebiusMu(3*d)^2:d in Divisors(n)]:n in [1..70]]; // _Marius A. Burtea_, Oct 19 2019
%Y A216913 Cf. A007947, A065463, A109007, A204455, A216914, A216919.
%K A216913 nonn,mult
%O A216913 1,2
%A A216913 _Peter Luschny_, Oct 02 2012