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 A267986 Perfect powers of the form x^2 + y^2 + z^2 where x > y > z > 0. 0
 49, 81, 121, 125, 169, 196, 216, 225, 243, 289, 324, 361, 441, 484, 529, 625, 676, 729, 784, 841, 900, 961, 1000, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1681, 1764, 1849, 1936, 2025, 2116, 2187, 2197, 2209, 2401, 2500, 2601, 2704, 2744, 2809, 2916, 3025, 3125, 3136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A001597 and A004432. 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, ... LINKS 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 Cf. A001597, A004432, A266927, A267321. Sequence in context: A036307 A294028 A056938 * A207638 A286095 A106311 Adjacent sequences:  A267983 A267984 A267985 * A267987 A267988 A267989 KEYWORD nonn AUTHOR Altug Alkan, Jan 23 2016 STATUS approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)