Let some number P be the product of two factors, A and B

Let the iterations of A*1..2..3..N up to B+1 be a directed graph.

Would this graph be eularian?

If so then it should be possible to use the BEST algorithm to count the number of eularian circuits, yielding B, no?

Edit: this is supported by the following text:

An arborescence can equivalently be defined as a rooted digraph in which the path from the root to any other vertex is unique.

* * *

Where the product of any two primes is unique, the path to it across our graph here, is also unique.