For n=3, 3circle configurations possess one dihedral symmetry D_{6}, or m = 3. Since a(n) must be <= 3 and also a multiple of m, a(n) = 3.
For n = 16, 16circle configurations have 6 D_{2m} symmetries with m >= 3.
Packing densities are for
m = 16: Pi/(2+2*csc(Pi/8)) = 0.43474+,
m = 15: (8*Pi/15)/(1+csc(2*Pi/15)) = 0.48445+,
m = 8: 4*sqrt(2)*Pi/(1+sqrt(2)+sqrt(3)+sqrt(42*sqrt(2)))^2 = 0.65004+,
m = 5: (16*Pi/5)*(73*sqrt(5))/sqrt(10+2*sqrt(5)) = 0.77110+,
m = 4: Pi/4 = 0.78539+,
m = 3: 8*Pi/(12+13*sqrt(3)) = 0.72813+.
The highest packing density is achieved at m = 4, or a(16) = 4.
Symmetry type (S) of ncircle configuration giving the highest packing density and the corresponding number of edges (N) of the regular polygon and packing density are given below. The packing configurations are illustrated in the Links.
n S N Packing density
   
3 D_{6} 3 Pi/(2+4/sqrt(3)) = 0.72900+
4,9,16 D_{8} 4 Pi/4 = 0.78539+
5 D_{10} 5 Pi/(2+8/sqrt(10+2*sqrt(5))) = 0.76569+
6 D_{6} 3 6*Pi/(12+7*sqrt(3)) = 0.78134+
7 D_{12} 6 7*Pi/(12+8*sqrt(3)) = 0.85051+
8 D_{14} 7 4*Pi/(7+7/sin(2*Pi/7)) = 0.78769+
10 D_{6} 3 5*Pi/(9+6*sqrt(3)) = 0.81001+
11 D_{10} 5 (22*Pi/25)/sqrt(10+2*sqrt(5)) = 0.72671+
12 D_{6} 6 6*Pi/(12+7*sqrt(3)) = 0.78134+
13 D_{12} 6 13*sqrt(3)*Pi/96 = 0.73685+
14 D_{14} 7 4*Pi/(sin(2*Pi/7)*(sqrt(3)+cot(Pi/7)+sec(Pi/7))^2) = 0.66440+
15 D_{6} 3 15*Pi/(24+19*sqrt(3)) = 0.82805+
17 D_{8} 4 (17*Pi/4)/(7+3*sqrt(2)+3*sqrt(3)+sqrt(6)) = 0.70688+
18 D_{12} 6 9*Pi/(12+13*sqrt(3)) = 0.81915+
19 D_{12} 6 19*Pi/(24+26*sqrt(3)) = 0.86465+
20 D_{8} 4 20*Pi/(2+sqrt(2)+2*sqrt(3)+sqrt(6))^2 = 0.72213+
21 D_{6} 3 21*Pi/(30+28*sqrt(3)) = 0.84045+
