A139266 Larger of two numbers in lowest terms whose sum, sum of squares and sum of cubes are all squares.

1, 345, 1562505, 184783370001360, 180972102858416484216240, 221277040503926652746669502425642824

Offset

0,2

Comments

To be in lowest terms the two numbers do not need to be coprime, but their highest common factor does need to be squarefree.

Links

Table of n, a(n) for n=0..5.

Andrew Bremner, "A Diophantine system", International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 2, pp. 413-415, 1986. doi:10.1155/S0161171286000522

Gentleman's Diary Problem (in Japanese)

sci.math discussion March 2008

Example

a(1)=345 since 184 and 345 have the properties 184+345=529=23^2, 184^2+345^2=152881=391^2 and 184^3+345^3=47293129=6877^2.

Crossrefs

Cf. A139265.

Sequence in context: A236731 A138043 A048904 * A063536 A045102 A225934

Adjacent sequences: A139263 A139264 A139265 * A139267 A139268 A139269

Keyword

nonn

Author

Henry Bottomley, Apr 13 2008

Status

approved