login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020898 Positive cubefree integers n such that the Diophantine equation X^3 + Y^3 = n*Z^3 has solutions. 11
2, 6, 7, 9, 12, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 34, 35, 37, 42, 43, 49, 50, 51, 53, 58, 61, 62, 63, 65, 67, 68, 69, 70, 71, 75, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 94, 97, 98, 103, 105, 106, 107, 110, 114, 115, 117, 123, 124, 126, 127, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These numbers are the cubefree sums of two nonzero rational cubes.

This sequence does not contain A202679, which has members that are not cubefree. - Robert Israel, Mar 16 2016

REFERENCES

B. N. Delone and D. K. Faddeev, The Theory of Irrationalities of the Third Degree, Amer. Math. Soc., 1964.

L. E. Dickson, History of The Theory of Numbers, Vol. 2, Chap. XXI, Chelsea NY 1966.

L. J. Mordell, Diophantine Equations, Ac. Press, Chap. 15.

LINKS

David W. Wilson, Table of n, a(n) for n = 1..255 (from Finch paper)

J. H. E. Cohn, The £ 450 question, Math. Mag., 73 (no. 3, 2000), 220-226.

Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]

Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]

EXAMPLE

37^3 + 17^3 = 6*21^3 is the smallest positive solution for n = 6 (found by Lagrange).

5^3 + 4^3 = 7*3^3 is the smallest positive solution for n = 7.

MATHEMATICA

(* A naive program with a few pre-computed terms *) nmax = 130; xmax = 2000; CubeFreePart[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 3]} & /@ FactorInteger[n]); nn = Reap[ Do[ n = CubeFreePart[ x*y*(x+y) ]; If[ 1 < n <= nmax, Sow[n]], {x, 1, xmax}, {y, x, xmax}]][[2, 1]] // Union; A020898 = Union[nn, {17, 31, 53, 67, 71, 79, 89, 94, 97, 103, 107, 123}](* Jean-François Alcover, Mar 30 2012 *)

CROSSREFS

Cf. A159843, A166246, A254324, A254326.

Sequence in context: A061416 A190247 A020897 * A184779 A200926 A047277

Adjacent sequences:  A020895 A020896 A020897 * A020899 A020900 A020901

KEYWORD

nonn,nice

AUTHOR

Steven Finch

EXTENSIONS

Entry revised by N. J. A. Sloane, Aug 12 2004

Links updated by Max Alekseyev, Oct 17 2007 and Dec 12 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 09:11 EDT 2019. Contains 327128 sequences. (Running on oeis4.)