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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. 2
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

Table of n, a(n) for n=1..2.

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

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

Sequence in context: A249966 A167823 A199099 * A296177 A206360 A292972

Adjacent sequences:  A251817 A251818 A251819 * A251821 A251822 A251823

KEYWORD

nonn,more,hard,bref

AUTHOR

Hartmut F. W. Hoft, Dec 09 2014

STATUS

approved

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Last modified September 25 12:16 EDT 2021. Contains 347654 sequences. (Running on oeis4.)