Not sum of three perfect powers: is the sequence infinite: sorry for misprinrs

[Giovanni Resta]

zak seidov wrote:

 >> Dear seqfans,
 >> 1) is this sequence infinite?
 >> 2) more terms?
 >> 3) thanks, zak
 >
 >
 >1,2,4,5,6,7,8,9,10,11,15,16,17,19,20,22,23,31,43,55,87,102,103,111,119,167,223,335,1391,1455,1607,1679,1775,1991,25887,26375

I believe that the sequence above (which should be a superset of A113505)
contains some spurious values, i.e.,
6, 9, 10, 11, 16, 17, 19, 20, 22, 43, 55, 102, 103, 223, 1775
since, for example, 6=4+1+1, 9=4+4+1, 10=8+1+1, 11=9+1+1, etc.etc.

the correct terms, below 106, seems to be:
1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119, 167, 335, 1391, 1455,
1607, 1679, 1991, 25887, 26375

I suspect that the sequence is indeed finite.

giovanni resta