# !Fancy sequence

Author: anonymous
Problem has been solved: 8 times

Русский язык | English Language

We call a sequence $Fancy$ if it consists only of digits and when summing all its elements, we get a number whose last digit does not occur among the elements of this sequence. Let $x$ be the number of ordered $Fancy$ sequences consisting of 666 elements. It is known that $x$ can be represented in the form $a^2 + b^2$, for some positive integers $a$ and $b$ such that $b$ takes the smallest possible value. Find the number of natural divisors of $ab$.