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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 (list; graph; refs; listen; history; text; internal format)
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, ...

LINKS

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

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 * A269390 A056875 A308011

Adjacent sequences:  A267309 A267310 A267311 * A267313 A267314 A267315

KEYWORD

nonn

AUTHOR

Altug Alkan, Jan 13 2016

STATUS

approved

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Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)