A271829 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.

81, 729, 2187, 2809, 3481, 5041, 6859, 14641, 15625, 19683, 24389, 26569, 27889, 59049, 63001, 68921, 83521, 148877, 273529, 300763, 332929, 357911, 375769, 413449, 531441, 597529, 619369, 657721, 683929, 704969, 707281, 744769, 776161, 779689, 844561, 877969, 912673

Offset: 1

Author

Altug Alkan, Apr 15 2016

Keywords

• nonn
• easy

Comments

Obviously, this sequence is infinite.

Intersection of A003072 and A025475.

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, ...

Examples

			81 is a term because 81 = 3^4 = 3^3 + 3^3 + 3^3.
		

Crossrefs

Cf. A003072, A007490, A025475.

Programs

Mathematica

Select[Range[10^6], And[! PrimeQ@ #, PrimePowerQ@ #, Length[PowersRepresentations[#, 3, 3] /. {0, } -> Nothing] > 0] &] (* Michael De Vlieger, Apr 17 2016 *)

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);