A134739 Cubes of (positive numbers that are not the sum of three nonzero squares), that is, the terms of A004214, cubed.

1, 8, 64, 125, 343, 512, 1000, 2197, 3375, 4096, 8000, 12167, 15625, 21952, 29791, 32768, 50653, 59319, 64000, 103823, 140608, 166375, 195112, 216000, 250047, 262144, 357911, 493039, 512000, 614125, 658503, 778688, 857375, 1000000

Offset

1,2

Comments

This sequence was inspired by e-mail from Ray Chandler, Nov 07 2007.

Original name was: Cubes which are not the sum of three nonzero squares. That definition would not include 125 = 5^2 + 6^2 + 8^2. - Robert Israel, Jan 12 2016

For "(cubes of positive numbers) that are not the sum of three nonzero squares", that is, the cubes in A004214, see A267189. - N. J. A. Sloane, Jan 18 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A004214(n)^3. - Ray Chandler, Jan 29 2009

Example

8 is in the sequence because it is not possible to express 2 as a sum of three nonzero squares and 2^3 = 8.
27 is not in the sequence because 3 = 1^2 + 1^2 + 1^2.

Maple

N:= 1000: # to get all terms <= N^3
A004214:= {$1..N} minus {seq(seq(seq(a^2 + b^2 + c^2, c = b .. floor(sqrt(N-a^2-b^2))), b = a .. floor(sqrt(N-a^2))), a=1..floor(sqrt(N/2)))}:
map(`^`, sort(convert(A004214, list)), 3); # Robert Israel, Jan 12 2016

Mathematica

searchMax = 16; Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, searchMax}]^3, x]], searchMax^2], 0]]^3 (* Based on Ray Chandler's program for A004214, Alonso del Arte, Jan 12 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=1, 1e3, if(!is(n), print1(n^3, ", "))); \\ Altug Alkan, Jan 13 2016

Crossrefs

Cf. A004214, A134738, A267189.

Sequence in context: A160428 A074102 A118719 * A116978 A125110 A209990

Adjacent sequences: A134736 A134737 A134738 * A134740 A134741 A134742

Keyword

nonn

Author

Artur Jasinski, Nov 07 2007

Extensions

Definition corrected by Robert Israel, Jan 12 2016

Status

approved