
EXAMPLE

The parts of the symmetric representations of sigma(15) and sigma(5950) are {8, 8, 8} and {4464, 4464, 4464}, respectively, so a(1) = 15 and a(2) = 5950.
Illustration of the symmetric representation of sigma(15) = 8 + 8 + 8 = 24 in the first quadrant:
.
. _ _ _ _ _ _ _ _ 8
. _ _ _ _ _ _ _ _
. 
. _ _
. _ _ 8
.  _
. _ _ 
. __ _ _ 8
.  
.  
.  
.  
.  
.  
.  
. _
.
The three parts have the same area.
(End)


MATHEMATICA

(* T[], row[], cD[] & tD[] are defined in A239663 *)
a251820[n_] := Module[{pT = T[n, 1], cT, cL, cW = 0, cR = 0, sects = {}, j = 1, r = row[n], test = True}, While[test && j <= r, cT = T[n, j+1]; cL = pT  cT; cW += (1)^(j+1) * tD[n, j]; If[cW == 0 && cR != 0, AppendTo[sects, cR]; cR = 0; If[Min[sects] != Max[sects], test = False], cR += cL * cW]; pT = cT; j++]; If[cW != 0, AppendTo[sects, 2 * cR  cW]]; Min[sects] == Max[sects] && Length[sects] > 1]
Select[Range[50000], a251820] (* data *)
