/
Divisibility.py
46 lines (36 loc) · 921 Bytes
/
Divisibility.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
from functools import cache
from _tabltypes import MakeTriangle
"""
The divisibility matrix, the indicator function for divisibility.
[ 0] 1
[ 1] 0 1
[ 2] 0 1 1
[ 3] 0 1 0 1
[ 4] 0 1 1 0 1
[ 5] 0 1 0 0 0 1
[ 6] 0 1 1 1 0 0 1
[ 7] 0 1 0 0 0 0 0 1
[ 8] 0 1 1 0 1 0 0 0 1
[ 9] 0 1 0 1 0 0 0 0 0 1
[10] 0 1 1 0 0 1 0 0 0 0 1
"""
@cache
def divisibility(n: int) -> list[int]:
if n == 0:
return [1]
L = [0 for _ in range(n + 1)]
L[1] = L[n] = 1
i = 1
div = n
while i < div:
div, mod = divmod(n, i)
if mod == 0:
L[i] = L[div] = 1
i += 1
return L
@MakeTriangle(divisibility, "Divisibility", ["A113704", "A051731"], True)
def Divisibility(n: int, k: int) -> int:
return divisibility(n)[k]
if __name__ == "__main__":
from _tabltest import TablTest
TablTest(Divisibility)