Marinada '21

[lang=hr] Prirodni broj nazivamo $n$\textit{-krakim} za $n \in \mathbb{N}$ ako se može zapisati kao zbroj $n$-tih potencija svojih znamenki. Na primjer, $1634$ je $4$-kraki broj jer je $1634=1^4+6^4+3^4+4^4$, dok je $1=1^n$ $n$-kraki broj za svaki $n$. \\ Koji je zbroj svih $5$-krakih brojeva? \\ [/lang] [lang=en] We say a natural number is $n$-pointed for $n \in \mathbb{N}$ if it can be written as the sum of $n^{\text{th}}$ powers of its digits. For example, $1634$ is a $4$-pointed number as $1634=1^4+6^4+3^4+4^4$, while $1=1^n$ is an $n$-pointed number for every $n$. \\ What is the sum of all $5$-pointed numbers? [/lang]