By setting \(f(p_n^k)=2^{2^{-n}}\) where \(p_n\) is the nth prime and then extending to a multiplicative function, one can get a strange construction of the Sierpinski triangle. The picture below does something with twin primes but it isn" t especially important, its just that the pattern still holds in this case. It&rsquo s a fun puzzle to figure out why (Here is a hint ).
