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A216913 a(n) = Gauss_primorial(3*n, 3) / Gauss_primorial(3*n, 3*n). 2

%I

%S 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 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 53,2,55,14,19,58,59,10,61,62,7,2,65,22,67,34,23,70,71

%N a(n) = Gauss_primorial(3*n, 3) / Gauss_primorial(3*n, 3*n).

%C The term Gauss primorial was introduced in A216914 and denotes the restriction of the Gauss factorial N_n! (see A216919) to prime factors.

%C Multiplicative because both A007947 and A109007 are. - _Andrew Howroyd_, Aug 02 2018

%H Andrew Howroyd, <a href="/A216913/b216913.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n/Sum_{k=1..3n} floor(cos^2(Pi*k^(3n)/(3n))). - _Anthony Browne_, May 24 2016

%F a(n) = A007947(n)/A109007(n). - _Andrew Howroyd_, Aug 02 2018

%F a(n) = Sum_{d|n} phi(d)*mu(3d)^2. - _Ridouane Oudra_, Oct 19 2019

%t Table[n/Sum[Floor[Cos[Pi k^(3 n)/(3 n)]^2], {k, 3 n}], {n, 71}] (* _Michael De Vlieger_, May 24 2016 *)

%o (PARI) a(n)={factorback(factor(n)[, 1])/gcd(3,n)} \\ _Andrew Howroyd_, Aug 02 2018

%o (Sage)

%o def Gauss_primorial(N, n):

%o return mul(j for j in (1..N) if gcd(j, n) == 1 and is_prime(j))

%o def A216913(n): return Gauss_primorial(3*n, 3)/Gauss_primorial(3*n, 3*n)

%o [A216913(n) for n in (1..80)]

%o (MAGMA) [&+[EulerPhi(d)*MoebiusMu(3*d)^2:d in Divisors(n)]:n in [1..70]]; // _Marius A. Burtea_, Oct 19 2019

%Y Cf. A007947, A109007, A204455, A216914, A216919.

%K nonn,mult

%O 1,2

%A _Peter Luschny_, Oct 02 2012

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)