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Originally Posted by biwema
Maybe I should have asked "Which is the first noninteger element of the sequence?"...
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Of course you could just follow the reference given in the OEIS:
http://links.jstor.org/sici?sici=000...3E2.0.CO%3B2-Z
(Example 25).
It's quite a worthwhile and enjoyable read.
The answer is that the 89th(!) number is not an integer.
EDIT: You'll also find that the same problem for
fourth powers yields a non-integer for the 97 number, for
fifth powers at the 214th position ...