19 можно ход только делителем

from functools import lru_cache


def moves(h):
    move = []
    for k in range(2, h + 1):
        if h % k == 0:
            move.append(h + h // k)
    return move


@lru_cache(None)
def game(h):
    if h >= 41:
        return 'win'
    elif any(game(m) == 'win' for m in moves(h)):
        return'p1'
    elif all(game(m) == 'p1' for m in moves(h)):
        return'v1'
    elif any(game(m) == 'v1' for m in moves(h)):
        return'p2'
    elif all(game(m) in ['p1', 'p2'] for m in moves(h)):
        return'v2'


def p19(h):
    return any(game(m) == 'p1' for m in moves(h))


print(len([s for s in range(1, 41) if p19(s)]))
print([s for s in range(1, 150) if (s % 3 != 0) and game(s) == 'p2'])
print([s for s in range(1, 150) if (s % 3 != 0) and game(s) == 'v2'])