Longest antichain of divisors I Need to find a way to calculate the length of the longest antichain of divisors of a number N (example 720 - 6, or 1450 - 4), with divisibility as operation.
Is there a universally applicable way to approach this problem for a given N?

If $N=\prod_p p^{e_p}$ is the prime factorization of $N$, then the longest such antichain has length $1+\sum_p e_p$ (if we count $N$ and $1$ as part of the chain, otherwise subtract $2$) and can be realized by dividing by a prime in each step.
Thus with $N=720=2^4\cdot 3^2\cdot 5^1$ we find $720\stackrel{\color{red}2}, 360\stackrel{\color{red}2}, 180\stackrel{\color{red}2}, 90\stackrel{\color{red}2}, 45\stackrel{\color{red}3}, 15\stackrel{\color{red}3}, 5\stackrel{\color{red}5}, 1$ 
and with $N=1450=2^15^229^1$ we find $1450\stackrel{\color{red}2},725\stackrel{\color{red}5},145\stackrel{\color{red}5},29\stackrel{\color{red}{29}}, 1$ (in red is the prime I divide by in each step; I start with the smallest, but the order does not matter).
