A267312 Integers n such that n^3 is the sum of 3 nonzero squares.

3, 5, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94, 96, 97, 98, 99, 100

Offset: 1

Author

Altug Alkan, Jan 13 2016

Keywords

• nonn

Comments

Motivation for this sequence is the equation n^3 = x^2 + y^2 + z^2 where x, y and z are nonzero integers.

Corresponding cubes are 27, 125, 216, 729, 1000, 1331, 1728, 2197, 2744, 4913, 5832, 6859, 8000, 9261, 10648, 13824, 15625, 17576, 19683, 24389, 27000, ...

Examples

			3 is a term because 3^3 = 27 = 1^2 + 1^2 + 5^2.
5 is a term because 5^3 = 125 = 5^2 + 6^2 + 8^2.
6 is a term because 6^3 = 216 = 2^2 + 4^2 + 14^2.
9 is a term because 9^3 = 729 = 2^2 + 10^2 + 25^2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000408.

Programs

Mathematica

Select[Range@ 100, Length[PowersRepresentations[#^3, 3, 2] /. {x_, , } /; x == 0 -> Nothing] != 0 &] (* Michael De Vlieger, Jan 13 2016 *)

PARI

is(n) = { my(a, b) ; a=1; while(a^2+1