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A134739 Cubes of (positive numbers that are not the sum of three nonzero squares), that is, the terms of A004214, cubed. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 20:24 EST 2018. Contains 318023 sequences. (Running on oeis4.)