A harmonic divisor number is a number whose factors have an integer harmonic mean. For example, 6 has factors 1, 2, 3, and 6, whose harmonic mean is 4/(1/1+1/2+1/3+1/6) = 2. In general, any perfect number is a harmonic divisor number, since the sum of reciprocals of divisors of a number n is equal to the sum of the divisors, divided by n, which is 2 for any perfect number, and the number of divisors of a perfect number is always even (since there are no square perfect numbers).