from lib_prime import primes
from functools import cache
from math import gcd


def get_phi_table(n: int, ps: list[int]) -> list[int]:
    tbl = [-1] * (n + 2)
    tbl[1] = 1
    queue = [(1, 1, 0)]

    while queue:
        x, phi, pi = queue.pop()
        for pin in range(pi, len(ps)):
            p = ps[pin]
            tbl[p] = p - 1
            xn = x * p
            if xn > n:
                break
            d = gcd(x, p)
            phid = tbl[d]
            assert phid != -1
            phin = (phi * (p - 1) * d) // phid
            tbl[xn] = phin
            queue.append((xn, phin, pin))
    return tbl


def euler_214():
    n = 40 * 10**6
    ps = primes(n)
    tbl = get_phi_table(n, ps)

    @cache
    def chain(n: int) -> int:
        if n == 1:
            return 1
        n = tbl[n]
        return 1 + chain(n)

    s = 0
    for i in range(len(ps)):
        p = ps[i]
        if chain(p) == 25:
            s += p
    return s


if __name__ == "__main__":
    solution = euler_214()
    print(f"e214.py: {solution}")
    assert solution == 1677366278943