Proposed sequence

[John Layman]

David Wilson wrote ( Mon, 17 Oct 2005 14:24:27 -0400):

To my knowledge, for n = 3 through 7, the smallest known integers that are 
a sum of two nth powers of positive rationals but not of two nth powers of 
positive integers are:

a(3) = 6 = (17/21)^3 + (37/21)^3
a(4) = 5906 = (25/17)^4 + (149/17)^4
a(5) = 68101 = (15/2)^5 + (17/2)^5
a(6) = 1124326946 = (73/5)^6 + (161/5)^6
a(7) = 69071941639 = (63/2)^7 + (65/2)^7


Me: This looked interesting, so I wrote a Mathematica program and soon found
a smaller value for n=6:

	164634913 = (44/5)^6 + (117/5)^6

I checked numerators to 200 and denominators to 50 and did not find a 
smaller value for n=7.

John W. Layman