First, generate an array (called values) that is 1 + 10^6 long which looks like the following: values = [0,1,1,1,1, .... ,1,1,1]
We will be building up the divisors of each number, n, where values[n] = sum of divisors n
Now create 2 nested loops, for variables x and y.
x go from 2 to 10^6 / 2
y go from 1 to 10^6 / x
loop through x then y, then values[x*y] += x, add a condiditon such that if x*y = x don't add it
This is because the index of values[x*y] is the number x*y, so clearly x is a divisor of x*y
For example lets calculate the sum of Divisors of 10:
We go through the loop and reach the following conditions
x = 2, y = 5, x*y = 10, so the number 10 has the divisor 2, and values = 1, so after addition values = 3
x = 5, y = 2, x*y = 10, so the number 10 has the divisor 5, and values = 3, so after addition values = 8
So now we see that for n=10, values = 1 + 2 + 5 = 8 which are the divisors of 10!
From there we can create the chains easily.
I will include a Divisors Function in my Essential Functions page
Enter a number (yourinput)
Code will output the minimum element of the longest chain with no element larger than yourinput