Chaotic Matrix

I expanded the matrix along the column $1$ .

Make all the elements in the first column of $A$ zero, except at the position $(x, 1)$ , and call the new matrix $D_{x, 1}$ . The following formula can be used to calculate the determinant of $D_{x,1}$ .

$|D_{x,1}| = -1 - \sum_{y} |D_{y,1}|$ where $y$ is a non-trivial positive divisor of $x$ .

Notice that the determinant of $D_{x, 1}$ does not depend on the size of the matrix. So, I stored the determinants of $D_{x, 1}$ in a list $d$ . This list can then be used to find the determinant of $A$ as follows.

$| A (n+1) | = | A (n) | + | D_{n, 1} |$

The value of the determinants are stored in the list $a$ .

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d = [0, 1, -1]
a = [0, 1, 0]

n = int(input("Size of the matrix... "))

for x in range(3, n+1):
    d.append(-1)
    for y in range(2, int(x/2)+1):
        if x % y == 0:
            d[x] -= d[y]

    a.append(a[-1] + d[-1])

for i, v in enumerate(a):
    print(i, v)

I use Mathcad. And find A028442