n = 3:
Networks with 3 unit resistors have A337517(3) = 4 resistance values: {1/3, 3, 3/2, 2/3}. The maximum product numerator X denominator is 6.
n = 6:
Networks with 6 unit resistors have A337517(6) = 57 resistance values, where 11/13 and 13/11 are the resistances with maximum product numerator X denominator.
+++
A   
/ \   
(1) / \ (2)  6 X 6  7 X 7 
/ \   
/ (3) \   
oo +++ 
\ //  ++++
\ (5)//  5 X 5   
(4) \ //(6)   4 X 4  4 X 4 
\ //    
Z ++++
___________________________________________________________________
Network with 6 unit resistors Corresponding rectangle tiling
total resistance 11/13 giving with 6 squares giving
a(6) = 11 X 13 = 143 A338861(6) = 143
n = 10:
With n = 10, nonplanarity comes in, yielding a(10) > A338861(10).
The "culprit" here is the network with resistance A338601(9)/A338602(9) = 130/101, giving a(10) = 13130 > A338861(10) = 10920.
n = 21:
The electrical network corresponding to the perfect squared square A014530 has specific voltage V_s equal to specific current A_s, namely V_s = A_s = 112. Its power V_s*A_s = 12544 is far below the maximum a(20) > a(10) > 13000, and a(n) is certainly monotonically increasing.  Rainer Rosenthal, Mar 28 2021
