

A088677


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


6



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
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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, 13091315, 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[(nx)^(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.
Sequence in context: A220229 A200890 A268265 * A321562 A034680 A017675
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



