A251820 Numbers n for which the symmetric representation of sigma(n) has at least 3 parts, all having the same area.

15, 5950

Offset: 1

Author

Hartmut F. W. Hoft, Dec 09 2014

Keywords

• nonn
• more
• hard
• bref

Comments

a(3) > 36000000.

Also intersection of A241558 and A241559 (minimum = maximum) minus the union of A238443 and A239929 (number of parts <= 2).

Examples

			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.
From _Omar E. Pol_, Dec 09 2014: (Start)
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)
		

Crossrefs

Cf. A000203, A237593, A237270, A238443, A239663, A241558, A241559.

Programs

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 *)