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%I #17 Apr 19 2016 16:14:17
%S 81,729,2187,2809,3481,5041,6859,14641,15625,19683,24389,26569,27889,
%T 59049,63001,68921,83521,148877,273529,300763,332929,357911,375769,
%U 413449,531441,597529,619369,657721,683929,704969,707281,744769,776161,779689,844561,877969,912673
%N Prime powers p^k such that p^k = x^3 + y^3 + z^3 where x, y, z are positive integers and k > 1, is soluble.
%C Obviously, this sequence is infinite.
%C Intersection of A003072 and A025475.
%C The first terms of this sequence are 3^4, 3^6, 3^7, 53^2, 59^2, 71^2, 19^3, 11^4, 5^6, 3^9, 29^3, 163^2, 167^2, 3^10, ...
%e 81 is a term because 81 = 3^4 = 3^3 + 3^3 + 3^3.
%t Select[Range[10^6], And[! PrimeQ@ #, PrimePowerQ@ #, Length[PowersRepresentations[#, 3, 3] /. {0, __} -> Nothing] > 0] &] (* _Michael De Vlieger_, Apr 17 2016 *)
%o (PARI) list(lim) = my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y),if(isprimepower(k+z^3) && !isprime(k+z^3), listput(v, k+z^3))))); Set(v);
%Y Cf. A003072, A007490, A025475.
%K nonn,easy
%O 1,1
%A _Altug Alkan_, Apr 15 2016
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