OFFSET
1,1
COMMENTS
Note that this sequence is not the complement of A267321. This sequence is a subsequence for complement of A267321.
Sequence focuses on the equation m^k = x^2 + y^2 + z^2 where x > y > z > 0 and m > 0, k >= 2.
Corresponding exponents are 2, 4, 2, 3, 2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2, 4, 2, 6, 2, 2, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 3, 2, 4, 2, 2, ...
EXAMPLE
49 is a term because 49 = 7^2 = 2^2 + 3^2 + 6^2.
81 is a term because 81 = 9^2 = 1^2 + 4^2 + 8^2.
121 is a term because 121 = 11^2 = 2^2 + 6^2 + 9^2.
MATHEMATICA
fQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[Range@ 1800, fQ@ # && Resolve[Exists[{x, y, z}, Reduce[# == x^2 + y^2 + z^2, {x, y, z}, Integers]]] &] (* Michael De Vlieger, Jan 24 2016, after Ant King at A001597 *)
PROG
(PARI) isA004432(n) = for(x=1, sqrtint(n\3), for(y=x+1, sqrtint((n-1-x^2)\2), issquare(n-x^2-y^2) && return(1)));
for(n=1, 1e4, if(isA004432(n) && ispower(n), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 23 2016
STATUS
approved