More numbers like 5906 (Terms of A060387 not in A003336)

[all at abouthugo.de]

SeqFans,

is there a chance to find more solutions to

x^4 + y^4 = c * z^4 with c > 1 and gcd(x,y,z)=1

The currently last term of
http://www.research.att.com/~njas/sequences/A060387
(x^4 + y^4 = n * z^4 is solvable in nonzero integers x,y,z)
is 5906, which is the first term differing from
http://www.research.att.com/~njas/sequences/A003336
(Numbers that are the sum of 2 nonzero 4-th powers)

5906*17^4 = 25^4 + 149^4 = 493275026

Without the requirement gcd(x,y,z)=1 the next solutions would be
6497   *   2^4   =  14^4   +   16^4      =          103952
6562   *   2^4   =   2^4   +   18^4      =          104992
6577   *   2^4   =   4^4   +   18^4      =          105232

I don't have access to the article mentioned in A003336, A060387
A. Bremner and P. Morton, A new characterization of the integer 5906, Manuscripta Math. 44 (1983) 187-229; Math. Rev. 84i:10016.

Does it say something on solutions to the problem above for c>5906?

If more solutions can be found then they would form a sequence passing the "is it interesting" test ;-).

Similar questions could be posed for the companion terms of
http://www.research.att.com/~njas/sequences/A111152
(Smallest number that is a sum of two n-th powers of positive rationals but not of two n-th powers of positive integers.), e.g. what is the next term
after 68101*2*5 = 15^5 + 17^5

Best regards

Hugo Pfoertner