cp's OEIS Frontend

A208191 Number of distinct 6-colored necklaces with n beads per color.

%I A208191 #12 Aug 23 2015 03:46:21
%S A208191 1,120,623760,7623616080,135277939358160,2961088201992945120,
%T A208191 74171603795480180204640,2041012695880532470281654960,
%U A208191 60192781171721237282811209918160,1872173374511564116503341160073744080,60735890264793885272652711347090416733760
%N A208191 Number of distinct 6-colored necklaces with n beads per color.
%H A208191 Alois P. Heinz, <a href="/A208191/b208191.txt">Table of n, a(n) for n = 0..70</a>
%F A208191 a(n) = Sum_{d|n} phi(n/d)*(6*d)!/(d!^6*6*n) if n>0 and a(0) = 1.
%F A208191 a(n) ~ 6^(6*n-1/2) / (2^(5/2) * Pi^(5/2) * n^(7/2)). - _Vaclav Kotesovec_, Aug 23 2015
%e A208191 a(0) =   1: the empty necklace.
%e A208191 a(1) = 120: {012345, 012354, ..., 054321}.
%p A208191 with(numtheory):
%p A208191 a:= n-> `if`(n=0, 1, add(phi(n/d) *(6*d)!/(d!^6 *6*n), d=divisors(n))):
%p A208191 seq(a(n), n=0..12);
%Y A208191 Column k=6 of A208183.
%Y A208191 Cf. A000010, A000142.
%K A208191 nonn
%O A208191 0,2
%A A208191 _Alois P. Heinz_, Feb 24 2012