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
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 07 2007
EXTENSIONS
Definition corrected by Robert Israel, Jan 12 2016
STATUS
approved