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A267312
Integers n such that n^3 is the sum of 3 nonzero squares.
1
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
1,1
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, ...
EXAMPLE
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.
MATHEMATICA
Select[Range@ 100, Length[PowersRepresentations[#^3, 3, 2] /. {x_, _, _} /; x == 0 -> Nothing] != 0 &] (* Michael De Vlieger, Jan 13 2016 *)
PROG
(PARI) is(n) = { my(a, b) ; a=1; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ; }
for(n=2, 1e2, if(is(n^3), print1(n, ", ")));
CROSSREFS
Cf. A000408.
Sequence in context: A098587 A321885 A161182 * A362579 A331386 A331916
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 13 2016
STATUS
approved