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A251820 Numbers n for which the symmetric representation of sigma(n) has at least 3 parts, all having the same area. 3
15, 5950 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(3) > 36000000.
Also intersection of A241558 and A241559 (minimum = maximum) minus the union of A238443 and A239929 (number of parts <= 2).
LINKS
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.
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)
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 *)
CROSSREFS
Sequence in context: A249966 A167823 A199099 * A296177 A206360 A292972
KEYWORD
nonn,more,hard,bref
AUTHOR
Hartmut F. W. Hoft, Dec 09 2014
STATUS
approved

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Last modified June 18 23:53 EDT 2024. Contains 373490 sequences. (Running on oeis4.)