ミュンヒハウゼン数

import itertools
import functools

@lru_cache(maxsize=1000)
def _calc(i, ind):
    return i * (10**ind)

def Munchhausen(n_digits=4):
    ret = []

    values = [(i, i**i) for i in range(1, 10)]
    for x in itertools.product(*[values]*n_digits):
        a = 0
        b = 0
        for ind, (i, iv) in enumerate(x):
            a += _calc(i, ind)
            b += iv
        if a == b:
            ret.append(a)
    return ret

for i in range(1, 7):
    print(i, Munchhausen(i))