# Four conditions

**Number Theory**Level 4

What is the smallest odd squarefree *abundant number*?

**Definition**:

An abundant number is a number for which the sum of its proper divisors is greater than the number itself. For example, the proper divisors of 12 are 1, 2, 3, 4, 6, and the sum of these proper divisor exceed the number 12, thus 12 is an abundant number.