A unitary divisor of a number n is a number d such that d|n and gcd(d, n/d)=1. For example, 3 is a unitary divisor of 12 because gcd(3, 12/3)=gcd(3, 4)=1.

A unitary perfect number is a number that is the sum of its unitary divisors less than itself. For example, 60 is a unitary perfect number because its unitary divisors less than itself are 1, 3, 4, 5, 12, 15, and 20, and 1+3+4+5+12+15+20=60. Find all unitary perfect numbers less than 1000000.