A088677 Numbers that can be represented as j^6 + k^6, with 0 < j < k, in exactly one way.

65, 730, 793, 4097, 4160, 4825, 15626, 15689, 16354, 19721, 46657, 46720, 47385, 50752, 62281, 117650, 117713, 118378, 121745, 133274, 164305, 262145, 262208, 262873, 266240, 277769, 308800, 379793, 531442, 531505, 532170, 535537, 547066

Offset

1,1

Comments

Conjecture: no number can be expressed as such a sum in more than one way.

Ekl (1996) has searched and found no solutions to the 6.2.2 Diophantine equation A^6 + B^6 = C^6 + D^6 with sums less than 7.25 * 10^26. - Jonathan Vos Post, May 04 2006

Links

Table of n, a(n) for n=1..33.

R. L. Ekl, New Results in Equal Sums of Like Powers, Math. Comput. 67, 1309-1315, 1998.

Eric Weisstein's World of Mathematics, Diophantine Equation: 6th Powers.

Example

65 = 1^6 + 2^6.

Mathematica

lst={}; e=6; Do[Do[x=a^e; Do[y=b^e; If[x+y==n, AppendTo[lst, n]], {b, Floor[(n-x)^(1/e)], a+1, -1}], {a, Floor[n^(1/e)], 1, -1}], {n, 2*8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 22 2009 *)

Prog

(PARI) powers2(m1, m2, p1) = { for(k=m1, m2, a=powers(k, p1); if(a==1, print1(k", ")) ); } powers(n, p) = { z1=0; z2=0; c=0; cr = floor(n^(1/p)+1); for(x=1, cr, for(y=x+1, cr, z1=x^p+y^p; if(z1 == n, c++); ); ); return(c) }

Crossrefs

Cf. A003358, A088719 (7th powers).

Sequence in context: A268265 A353939 A351269 * A321562 A034680 A351301

Adjacent sequences: A088674 A088675 A088676 * A088678 A088679 A088680

Keyword

nonn

Author

Cino Hilliard, Nov 22 2003

Extensions

Edited by Don Reble, May 03 2006

Status

approved