The original definition was "Numbers whose fifth powers have a partition as a sum of fifth powers of five nonzero integers". But all nonnegative numbers should be in this sequence, since e.g. n^5 = (412 n)^5 + (310 n)^5 + (16 n)^5 + (-127 n)^5 + (-430 n)^5. - Robert Israel, Sep 01 2015