Let's take two numbers A and B, and take their prime factorizations
$A=p_1^{a_1}\cdot p_2^{a_2}\cdot\dots \cdot p_n^{a_n}$
B=p_1^{a'_1}\cdot p_2^{a'_2}\cdot\dots\cdot p_n^{a'_n}
Now similarity of two numbers is simply
\sum_{i=1}^{\infty}|a_i-a'_i|
It's very easy to make it work and take similarity of two numbers using Eratosthenes sieve, but are there any properties of such "similarity"?
For example having numbers $A,B,C$ Is there other way to know to which number, number A is the most similar (excluding number A of course), then simply computing this similarity with every possible number?
Chris