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

[Giovanni Resta]

Max Alekseyev wrote:

 > But 1 is not a perfect power. See
 > http://www.research.att.com/~njas/sequences/A072103

The sequence you cited above says:
A072103 Sorted perfect powers a^b for a, b > 1 with duplication.

so it consists of those perfect powers for which both the base
and the exponent are greater than 1. It does not seems
to me to be the "definition" of perfect power.

I have always considered 1 as a square, a cube, etc.etc.
so for me it is a perfect power.

But of course you are free to use your own definition of "perfect power".

By the way, I've further checked Zak's sequence and it does not contains
other values up to 10^9.

It is interesting to note that, even restricting the usable
powers to squares and cubes, the resulting sequence of
missing sums seems finite. Up to 10^9 I have:
1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119, 148, 167, 263, 311, 335,
391, 407, 455, 559, 599, 839, 951, 1159, 1231, 1287, 1303, 1391,
1455, 1463, 1607, 1660, 1679, 1751, 1863, 1991, 2351, 2615, 2799,
3247, 3983, 4327, 4367, 5199, 5655, 6047, 6159, 6351, 6599, 6663,
7367, 7495, 7503, 8087, 9519, 10823, 11535, 13415, 13559, 16391,
17135, 17887, 18599, 21727, 24655, 25887, 26375, 27103, 27887, 36959,
37471, 40079, 42503, 50063, 55327, 97231, 98447, 103543, 104159,
112055, 192471

bye,
giovanni