Landau's Function

landau.py

from math import gcd
from functools import reduce
from typing import Iterator

def lcm(nums: list[int]) -> int:
    _lcm = lambda a, b: (a * b) // gcd(a, b)
    return reduce(_lcm, nums)

def partitions(n: int, s: int = 1) -> Iterator[int]:
    yield (n,)
    for i in range(s, n // 2 + 1):
        for p in partitions(n - i, i):
            yield (i,) + p

def landau(n: int) -> int:
    return max(lcm(p) for p in partitions(n))

for i in range(1, 50):
    print(f"g({i})={landau(i)}")