Problem 119

Digit power sum

The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 8³ = 512. Another example of a number with this property is 614656 = 28⁴.

We shall define a_n to be the n^th term of this sequence and insist that a number must contain at least two digits to have a sum.

You are given that a₂ = 512 and a₁₀ = 614656.

Find a₃₀.

数字和的幂

512是一个有趣的数，因为它等于其各位数字和的幂：5 + 1 + 2 = 8，而8³ = 512。拥有同样性质的数的另一个例子是614656 = 28⁴。

记a_n是这类数中的第n个，并且约定一个数至少需要两位数字才有各位数字和。

已知a₂ = 512以及a₁₀ = 614656。

求a₃₀。