def divisors(n):
    summ = 0
    for i in range(1, n//2+1):
        if n%i==0:
            summ = summ + i
    return summ

def number_type (n):
    summ = divisors(n)
    if summ == n:
        return 'perfect'
    elif summ < n:
        return 'deficient'
    else:
        return 'abundant'

def are_friends (n, m):
    return divisors(n) == m and divisors(m) == n