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A134341 Numbers whose fifth powers have a partition as a sum of fifth powers of four positive integers. 2
144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440, 1584, 1728, 1872, 2016, 2160, 2304, 2448, 2592, 2736, 2880, 3024, 3168, 3312, 3456, 3600, 3744, 3888, 4032, 4176, 4320, 4464, 4608, 4752, 4896, 5040, 5184, 5328, 5472, 5616, 5760, 5904, 6048, 6192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..43.

L. J. Lander and T. R. Parkin, Counterexample to Euler's conjecture on sums of like powers, Bull. Amer. Math. Soc. 72 (6) (1966), p. 1079.

Burkard Polster, Euler's and Fermat's last theorems, the Simpsons and CDC6600 - Mathologer, 2018.

Wikipedia, Euler's sum of powers conjecture

FORMULA

a(n) = 144*k if n is not congruent to 0 mod 593 or a(n) = 85359*j when n is congruent to 0 mod 593 {where k,j successive integers}.

EXAMPLE

a(1) = 144 because 144^5= 27^5 + 84^5 + 110^5 + 133^5;

a(593) = 85359 because 85359^5 = 55^5 + 3183^5 + 28969^5 + 85282^5 = 4531548087264753520490799 (Jim Frye 2005) (Typo corrected by Sebastien Palcoux, Jul 05 2017).

CROSSREFS

Cf. A134297, A134298, A134341, A003828, A175610.

Sequence in context: A008436 A250773 A262245 * A125841 A154051 A217584

Adjacent sequences:  A134338 A134339 A134340 * A134342 A134343 A134344

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 21 2007

STATUS

approved

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Last modified June 21 14:00 EDT 2018. Contains 305620 sequences. (Running on oeis4.)