Problem

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2016

Tags: Coloring, greatest common divisor, combinatorics



We color numbers $1,2,3,...,20$ in two colors, blue and yellow, such that both colors are used (not all numbers are colored in one color). Determine number of ways we can color those numbers, such that product of all blue numbers and product of all yellow numbers have greatest common divisor $1$.