Isn't that just the sum of divisors of the radical of n? The radical of n is the product of the distinct prime divisors of n. For example, for , . The divisors of n are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 of which 1, 2, 3, 6, 7, 14, 21, and 42 are square free. This is exactly the set of divisors of 42.