Camacho numbers are positive integers that are equal to the sum of their digits raised to each power from 1 to the number of digits. For a Camacho number $n\in {\mathbb{N}}_0$ that consists of the digits $d_1{d}_2\dots d_m$, it must therefore hold that $$\sum _{p=1}^m(d_1^p+d_2^p+\cdots +d_m^p)=n$$

For example, 336 is a Camacho number because $$(3+3+6)+(3^2+3^2+6^2)+(3^3+3^3+6^3)=336$$

Assignment

• Write a function camacho_term that takes two integers $n,p\in {\mathbb{N}}_0$ (int). If $n$ consists of the digits $d_1{d}_2\dots d_m$, the function must return the result (int) of the following expression: $$d_1^p+d_2^p+\cdots +d_m^p$$

• Write a function camacho_sum that takes an integer $n\in {\mathbb{N}}_0$ (int). If $n$ consists of the digits $d_1{d}_2\dots d_m$, the function must return the result (int) of the following expression: $$\sum _{p=1}^m(d_1^p+d_2^p+\cdots +d_m^p)$$

• Write a function iscamacho that takes an integer $n\in {\mathbb{N}}_0$ (int). The function must return a Boolean value (bool) that indicates if $n$ is a Camacho number.

• Write a function next_camacho that takes an integer $n\in {\mathbb{N}}_0$ (int). The function must return the smallest Camacho number (int) that is greater than $n$.

Example

                
            >>> camacho_term(336, 1)
12
>>> camacho_term(336, 2)
54
>>> camacho_term(336, 3)
270

>>> camacho_sum(336)
336
>>> camacho_sum(4538775)
4538775
>>> camacho_sum(183670618569)
499096875990

>>> iscamacho(336)
True
>>> iscamacho(4538775)
True
>>> iscamacho(183670618569)
False

>>> next_camacho(60)
90
>>> next_camacho(4537541)
4538775
>>> next_camacho(183670618569)
183670618662