Base Tree

Building up from the number one all odd numbers are connect to a 4mod6 number.  All 4mod6 can be divided once and 2mod6 can be divided once again.  Both Divide columns have matching numbers in the odd column or the even column except for 2mod6 numbers because they are linked to a odd number.  The last divide/2 is the number matching the first 2 columns.  There are no 0mod6 numbers because they are not reachable from any odd number. They all divide into the 3mod6 numbers that only show up for their branch connections.

You can use this to go forward to any number or run the number as normal down to the number 1