contracted version of A046074

[Max A.]

For which n, there exists an integer greater than 1 equal to the sum
of n-th power of its decimal digits?
The sequence of such n corresponds to the contraction of A046074. It
is also a sequence of those n such that A003321(n) > 0. From A003321
we can derive the beginning of this sequence:
1,3,4,5,6,7,8,9,10,11,13,14,16,17

Rustem Aidagulov has found a 52-digit monster
3009336689622424785094591221547283824126694123199598 which is the sum
of the 53-rd power of its digits implying that 53 belongs to the
sequence in question (as well as to A046074).

Max