In the blocks that come before,
their special product tells us more.
To guess my scheme you'll need calculation,
but only little tests of recreation.
Each block contains atoms strong as Thor,
which further join to make a score.
Yet some atoms die if they do not share,
no paths to find without a care.
What finally joins must have intersection,
in order to make my fine collection.
I'm a number with a special product,
so name me when you think you've got it.
from math import factorial from itertools import combinations
Make use of prime factors.
The factors of a factorial that are used to calculate the factorial can form a set.
The path weights represent the number of times that something is shared, with edges of weight 0 being dropped out of the graph altogether.
We might consider a subset of the Cartesian product of factors that are used to calculate a number.